AP Physics 1 Summer Work 2018

Transcription

1 AP Physics 1 Summer Work 018 The purpose of this long-term assignment is to make sure everyone begins the year with the same minimum knowledge of physics and the math necessary to do physics. Some of you will find that you have to learn some things on your own, and some of you will find that this is review. In either case, everyone is required to read through the material in this packet and complete the Take Home Test before the start of school. The Practice Test is due on the first day of class. This assignment is meant to be completed over a period of time. Do not wait until the very end of summer vacation to begin! I encourage you to work together, but please do not just copy answers. Ultimately, you are responsible for the material. Send me an so that I have your address and can make an AP Physics 1 list. (b_lengas@sharon.k1.ma.us). What s in this packet.... Mathematical Concepts Dimensional Analysis Trigonometry Scalars and Vectors Vector Addition & Subtraction Vector Components Vector Addition using Components One-Dimensional Kinematics Definitions and Equations Problem Solving Strategy Graphical Analysis Pages - 9 Pages Practice Test Pages 18-9 AP Physics 1 Page 1

2 Mathematical Concepts DIMENSIONAL ANALYSIS All physical quantities have units so that we can communicate their measurement. IN the metric system, the base units are called SI units. The base SI units for the fundamental quantities of mass, length, and time are the kilogram, meter, and second, respectively. Any unit which is a combination of these fundamental units is called a derived unit. An example of a derived unit would be meters/second or kilometers/hour, which are both units for speed. Sometimes we will need to convert from one unit to another. Example 1 Convert 80.0 km/h to m/s. km 1000 m 1h m h = 1km 3600 s s Note that we multiplied 80.0 km/h by two quotients which were each equal to one, so we didn t change the value of the speed, we only expressed it in different units. Dimensional Analysis Often you will need to be able to determine the validity of equations by analyzing the dimensions of the quantities involved. Example Verify that the equation below is valid by using dimensional analysis. ( ) FΔ t = m v f v 0 where F is force measured in Newtons, t is time in seconds, m is mass in kg, and v is speed in m/s. kg m We will show later that a Newton =. Thus the units for each side of the equation can be s written as kg m m m s = kg s s s kg m kg m = s s AP Physics 1 Page

3 TRIGONOMETRY Trigonometry is the study of triangles, and often right triangles. The lengths of the sides of a right triangle can be used to define some useful relationships, called the sine, cosine, and tangent, abbreviated sin, cos, and tan, respectively. Example 3 A ball on the end of a string of length L = 0.50 cm is hung from a hook in the ceiling. The ball is pulled back to an angle θ = 30º from the vertical. What is the height h above the lowest point of the ball? L θ L h If we draw a horizontal line from the raised ball to form a right triangle, the portion of the vertical line above the horizontal line forms the adjacent side of the right triangle. This length would then be Lcosθ. L θ L Lcosθ h = L - Thus the height h would be the difference between L and Lcosθ: ( 1 ) h = L Lcosθ = L cosθ The trigonometric relationships listed in the Equations and Symbols section will be particularly helpful when dealing with vectors. AP Physics 1 Page 3

4 SCALARS AND VECTORS A scalar is a quantity which has no direction associated with it, such as mass, volume, time, and temperature. We say that scalars have only magnitude, or size. A mass may have a magnitude of kilograms, a volume may have a magnitude of 5 liters, and so on. But a vector is a quantity which has both magnitude (size) and direction (angle). For example, if someone tells you they are going to apply a 0 pound force on you, you would want to know the direction of the force, that is, whether it will be a push or a pull. So, force is a vector, since direction is important in specifying a force. The same is true of displacement, as we will see in the following sections. The table below lists some vectors and scalars you will be using in your physics course. Vectors displacement velocity acceleration force weight momentum Scalars distance speed mass time volume temperature work and energy VECTOR ADDITION AND SUBTRACTION We can graphically add vectors to each other by placing the tail of one vector onto the tip of the previous vector: R A R = A + B B R A - R = A + (- B), or R = A B In the diagram on the left above, we have added two vectors head to tail by placing the tail of vector B on the head (tip) of vector A. When adding vectors graphically, we may move a vector anywhere we like, but we must not change its length or direction. The resultant is drawn from the tail of the first vector to the head of the last vector. The resultant is also called the vector sum of A and B, and can replace the two vectors and yield the same result. AP Physics 1 Page 4

5 Example: Displacement is also a vector. Consider a hiker who walks 8 kilometers due east, then 10 km due north, then 1 km due west. What is the hiker s displacement from the origin? A vector can be represented by an arrow whose length gives an indication of its magnitude (size), with the arrow tip pointing in the direction of the vector. We represent a vector by a letter written in bold type. For this example, we list the displacement vectors like this: A = 8 km west B = 10 km north C = 1 km east We can graphically add the second displacement vector to the first, and the third displacement vector to the second: 1 km N W 10 km R = 10.8 km at 68º from E 68º E 8 km S The resultant vector is the displacement from the origin to the tip of the last vector. In other words, the resultant is the vector sum of the individual vectors, and can replace the individual vectors and end up with the same result. Of course, just adding the lengths of the vectors together will not achieve the same result. Adding 8 km, 10 km, and 1 km gives 30 km, which is the total distance traveled, but not the straight-line displacement from the origin. We see in the diagram above that the resultant displacement is 10.8 km from the origin at an angle of 68º from the east axis. AP Physics 1 Page 5

6 We could have added the displacements in any order and achieved the same resultant. We say that the addition of vectors is commutative. The equilibrant is the vector which can cancel or balance the resultant vector. In this case, the equilibrant displacement is the vector which can bring the hiker back to the origin. Thus, the equilibrant is always equal and opposite to the resultant vector. N 1 km W 10 km 8 km 68º E = - R = 10.8 km at 68º + 180º from E E S AP Physics 1 Page 6

7 COMPONENTS OF A VECTOR We may also work with vectors mathematically by breaking them into their components. A vector component is the projection or shadow of a vector onto the x- or y-axis. For example, let s say we have two vectors A and B shown below: A y A B y B α A x φ B x We will call the projection of vector A onto the x-axis its x-component, A x. Similarly, the projection of A onto the y-axis is A y.the vector sum of A x and A y is A, and, since the magnitude of A is the hypotenuse of the triangle formed by legs A x and A y, the Pythagorean theorem holds true: A = A x + A y and from the figures above, A x = Asinα A y = Acosα tanα = A A y x We can write the same relationships for vector B by simply replacing A with B and the angles α with φ in each of the equations above. AP Physics 1 Page 7

8 Example: Find the x- and y-components of the resultant in the previous example. The resultant is 10.8 km long at an angle of 68º from the east (+x) axis: Since the vector component R x is adjacent to the 68º angle, we have the relationship R x = Rcosθ = (10.8 km)cos 68º = 4 km R y R Similarly, the vector component R y is opposite to the 68º angle, so we have R y = Rsinθ = (10.8 km)sin 68º = 10 km 68º R x VECTOR ADDITION BY MEANS OF COMPONENTS Earlier we added vectors together graphically to find their resultant. Using the head-to-tail method of adding vectors, we can find the resultant of A and B, which we called R. We can also use components to find the resultant of any number of vectors. For example, the x-components of the resultant vector R is the sum of the x-components of A, B, and C. Similarly, The y- components of the resultant vector R is the sum of the y-components of A and B. So, we have that R x = A x + B x + C x and R y = A y + B y + C y and by the Pythagorean theorem, x y R = R + R + R z Example: Using the diagrams below, let A = 4 meters at 30º from the x-axis, B = 3 meters at y 45º from the x-axis, and C = 5 m at 5º from the y-axis. Find the magnitude and direction of the resultant vector R. (cos30 = 0.87, sin 30 = 0.50, cos45 = sin45 = 0.70, B cos5 = 0.90, sin5 = 0.4) A x C AP Physics 1 Page 8

9 Solution: First, we need to find A x, A y, B x, B y, C x, and C y : A x = Acos30 = (4 m)cos30 = (4 m)(0.87) = 3.5 m. A y = Asin30 = (4 m)cos30 = (4 m)(0.50) =.0 m B x = Bcos45 = (3 m)cos45 = (3 m)(0.70) =.1 m B y = Bsin45 = (3 m)sin45 = (3 m)(0.70) =.1 m C x = - Csin5 = (5 m)sin5 = - (5 m)(0.43) = -. m C y = - Ccos5 = (5 m)cos5 = - (5 m)(0.90) = m Note that C x and C y are both negative, since they point to the left and down, respectively. Now we can find the x- and y-components of the resultant R: R x = A x + B x + C x = 3.5 m +.1 m + (-. m) = 3.4 m R y = A y + B y + C y =.0 m +.1 m + (- 4.5 m) = -0.4 m The magnitude of the resultant C is R =. m at 60º from the +x-axis = = ( 1.1m) + ( 1.9 m) =. m R R x + R y and its angle from the x-axis can be found by tanθ = R R y x 1.9 m θ = tan 1 = m R = 3.4 m at 6.7 below + x-axis The properties of vectors we ve discussed here can be applied to any vector, including velocity, acceleration, force, and momentum. AP Physics 1 Page 9

10 ONE DIMENSIONAL KINEMATICS DISPLACEMENT Distance d can be defined as total length moved. If you run around a circular track, you have covered a distance equal to the circumference of the track. Distance is a scalar, which means it has no direction associated with it. Displacement Δx, however, is a vector. Displacement is defined as the straight-line distance between two points, and is a vector which points from an object s initial position x o toward its final position x f. In our previous example, if you run around a circular track and end up at the same place you started, your displacement is zero, since there is no distance between your starting point and your ending point. Displacement is often written in its scalar form as simply Δx or x. SPEED AND VELOCITY Average speed is defined as the amount of distance a moving object covers divided by the amount of time it takes to cover that distance: average speed = v = distance elapsed time d = t where v stands for speed, d is for distance, and t is time. Average velocity is defined a little differently than average speed. While average speed is the total change in distance divided by the total change in time, average velocity is the displacement divided by the change in time. Since velocity is a vector, we must define it in terms of another vector, displacement. Oftentimes average speed and average velocity are interchangeable for the purposes of the AP Physics B exam. Speed is the magnitude of velocity, that is, speed is a scalar and velocity is a vector. For example, if you are driving west at 50 miles per hour, we say that your speed is 50 mph, and your velocity is 50 mph west. We will use the letter v for both speed and velocity in our calculations, and will take the direction of velocity into account when necessary. ACCELERATION Acceleration tells us how fast velocity is changing. For example, if you start from rest on the goal line of a football field, and begin walking up to a speed of 1 m/s for the first second, then up to m/s, for the second second, then up to 3 m/s for the third second, you are speeding up with an average acceleration of 1 m/s for each second you are walking. We write Δv 1m / s m a = = = 1m / s / s = 1 Δt 1s s AP Physics 1 Page 10

11 In other words, you are changing your speed by 1 m/s for each second you walk. If you start with a high velocity and slow down, you are still accelerating, but your acceleration would be considered negative, compared to the positive acceleration discussed above. Usually, the change in speed Δv is calculated by the final speed v f minus the initial speed v o. The initial and final speeds are called instantaneous speeds, since they each occur at a particular instant in time and are not average speeds. APPLICATIONS OF THE EQUATIONS Assume Uniform Acceleration Kinematics is the study of the relationships between distance and displacement, speed and velocity, acceleration, and time. The kinematic equations are the equations of motion which relate these quantities to each other. These equations assume that the acceleration of an object is uniform, that is, constant for the time interval we are interested in. The kinematic equations listed below would not work for calculating velocities and displacements for an object which is accelerating erratically. v vo a = t v = v + at 1 Δx = ( vo + v) t 1 Δx = vot + at v o = v o + aδx where Δx = displacement (final position initial position) v = velocity or speed at any time v o = initial velocity or speed t = time a = acceleration AP Physics 1 Page 11

12 Freely Falling Bodies An object is in free fall if it is falling freely under the influence of gravity. Any object, regardless of its mass, falls near the surface of the Earth with an acceleration of 9.8 m/s, which we will denote with the letter g. We will round the free fall acceleration g to 10 m/s for the purpose of the AP Physics B exam. This free fall acceleration assumes that there is no air resistance to impede the motion of the falling object, and this is a safe assumption on the AP Physics B test unless you are told differently for a particular question on the exam. Since the free fall acceleration is constant, we may use the kinematic equations to solve problems involving free fall. We simply need to replace the acceleration a with the specific free fall acceleration g in each equation. Remember, anytime a velocity and acceleration are in opposite directions (like when a ball is rising after being thrown upward), you must give one of them a negative sign. Example 1 A girl is holding a ball as she steps onto a tall elevator on the ground floor of a building. The girl holds the ball at a height of 1 meter above the elevator floor. The elevator begins accelerating upward from rest at 3 m/s. After the elevator accelerates for 5 seconds, find (a) the speed of the elevator (b) the height of the floor of the elevator above the ground. At the end of 5 s, the girl lets go of the ball from a height of 1 meter above the floor of the elevator. If the elevator continues to accelerate upward at 3 m/s, describe the motion of the ball (c) relative to the girl s hand, (d) relative to the ground. (e) Determine the time after the ball is released that it will make contact with the floor. (f) What is the height above the ground of the ball and floor when they first make contact? AP Physics 1 Page 1

13 Solution: (a) v = vo + at = 0 + ( 3m / s )( 5s) = 15 m / s upward (b) y v t 1 1 = o + at = 0 + ( 3m / s )( 5s) = 37. 5m (c) When the girl releases the ball, both she and the ball are moving with a speed of 15 m/s upward. However, the girl continues to accelerate upward at 3 m/s, but the ball ceases to accelerate upward, and the ball s acceleration is directed downward at g = 10 m/s, that is, it is in free fall with an initial upward velocity of 15 m/s. Therefore the ball will appear to the girl to fall downward with an acceleration of 3 m/s (- 10 m/s ) = 13 m/s downward, and will quickly fall below her hand. (d) Someone watching the ball from the ground would simply see the ball rising upward with an initial velocity of 15 m/s, and would watch it rise to a maximum height, at which point it would be instantaneously at rest (provided it doesn t strike the floor of the elevator before it reaches its maximum height). (e) When the ball is released, it is traveling upward with a speed of 15 m/s, has a downward acceleration of 13 m/s relative to the floor, and is at a height y = 1 m above the floor. The time it takes to fall to the floor is 1 y = at 1 1m = t = 0.4 s ( 13m / s ) t (f) In this time of 0.4 s, the elevator floor has moved up a distance of 1 1 Δ y = aet = ( 3m / s )( 0.4s) = 0. 4 m Thus, the ball and elevator floor collide at a height above the ground of 37.5 m m = m. AP Physics 1 Page 13

14 GRAPHICAL ANALYSIS OF VELOCITY AND ACCELERATION Let s take some time to review how we interpret the motion of an object when we are given the information about it in graphical form. On the AP Physics B exam, you will need to be able to interpret three types of graphs: position vs.time, velocity vs. time, and acceleration vs. time. Position vs. time Consider the position vs. time graph below: x (m) Δ x (m) P Δ Δt t (s) t (s) Δt Δ x The slope of the graph on the left is, and is therefore velocity. The curved graph on the Δt right indicates that the slope is changing. The slope of the curved graph is still velocity, even though the velocity is changing, indicating the object is accelerating. The instantaneous velocity at any point on the graph (such as point P) can be found by drawing a tangent line at the point and finding the slope of the tangent line. AP Physics 1 Page 14

15 Velocity vs. time Consider the velocity vs. time graph below: v Δ v Δt t (s) Are t (s) Δ v As shown in the figure on the left, the slope of a velocity vs. time graph is, and is therefore Δt acceleration. As shown on the figure on the right, the area under a velocity vs. time graph would m have units of ( s) = m, and is therefore displacement. s Acceleration vs. time Since in this class we will generally deal with constant acceleration, any graph of acceleration vs. time on the exam would likely be a straight horizontal line: a (m/s ) +5 m/s a (m/s ) 0 t(s) -5 m/s 0 t(s) This graph on the left tells us that the acceleration of this object is positive. If the object were accelerating negatively, the horizontal line would be below the time axis, as shown in the graph on the right. AP Physics 1 Page 15

16 Example Consider the position vs. time graph below representing the motion of a car. Assume that all accelerations of the car are constant. H I J x(m ) F 0 t(s) K A Practice: On the axes on the next page, sketch the velocity vs. time and acceleration vs. time graphs for this car. v(m/s 0 t(s) a(m/s 0 t(s) AP Physics 1 Page 16

17 Solution: The car starts out at a distance behind our reference point of zero, indicated on the graph as a negative displacement. The velocity (slope) of the car is initially positive and constant from points A to C, with the car crossing the reference point at B. Between points C and D, the car goes from a high positive velocity (slope) to a low velocity, eventually coming to rest (v = 0) at point D. At point E the car accelerates positively from rest up to a positive constant velocity from points F to G. Then the velocity (slope) decreases from points G to H, indicating the car is slowing down. It is between these two points that the car s velocity is positive, but its acceleration is negative, since the car s velocity and acceleration are in opposite directions. The car once again comes to rest at point H, and then begins gaining a negative velocity (moving backward) from rest at point I, increasing its speed negatively to a constant negative velocity between points J and K. At K, the car has returned to its original starting position. The velocity vs. time graph for this car would look like this: v(m/s B C F G A 0 D E H I t(s) J K The acceleration vs. time graph for this car would look like this: a(m/s E F A B C D 0 G H I J K t(s) AP Physics 1 Page 17

18 AP PHYSICS 1 PRACTICE TEST DUE DATE: The first day of class! Name: Part I. Multiple Choice. Read each question carefully and write the capital letter of the best choice in the blank at left. Show calculations to the right of the question. 1. The fundamental SI units for mass, length, and time, respectively are (A) newton, meter, minute (B) kilogram, meter, second (C) pound, foot, hour (D) pound, foot, second (E) kilogram, centimeter, hour. How many nanometers are in a kilometer? (A) 10-9 (B) 10 9 (C) 10-1 (D) 10 1 (E) The data plotted on a graph of distance on the y-axis vs time on the x-axis yields a linear graph. The slope of the graph is Δd (A) Δt (B) (Dd)( Dt) Δt (C) Δd (D) (Dd) + ( Dt) (E) (Dd) - ( Dt) 4. Consider the velocity vs time graph shown. The area under the graph from s to 6 s is most nearly (A) 8 (B) 16 (C) 4 (D) 3 (E) 36 AP Physics 1 Page 18

19 5. Data from an experiment shows that potential energy is proportional to the square of displacement. The plot of the graph of potential energy (y) vs. displacement (x) would be (A) a straight horizontal line (B) a straight diagonal line sloping upward (C) a parabola (D) a hyperbola (E) a circle 6. The cosine of an acute angle in a right triangle is equal to the (A) sine of the angle (B) tangent of the angle (C) the hypotenuse of the triangle (D) the side adjacent to the angle (E) the ratio of the side adjacent to the angle and the hypotenuse of the triangle 7. Which of the following quantities is NOT a vector quantity? (A) displacement (B) mass (C) resultant (D) equilibrant (E) 10 km at 30 north of east 8. The resultant of the two displacement vectors 30 m east and 40 m south is (A) 50 m southeast (B) 70 m northeast (C) 10 m southwest (D) 10 m northeast (E) 10 m northeast 9. The x-component of the vector shown to the right is most nearly (A) 100 m (B) 50 m y (C) 87 m (D) 58 m 100 m (E) 1000 m 30 x AP Physics 1 Page 19

20 10. Two displacement vectors each having a y-component of 100 km are added together vectorially to form a resultant which forms an angle of 60 from the +x-axis. What is the magnitude of the resultant? (A) 30 m (B) 400 m (C) 10 m (D) 00 m (E) 300 m 11. Which of the following statements is true? (A) Displacement is a scalar and distance is a vector. (B) Displacement is a vector and distance is a scalar. (C) Both displacement and distance are vectors. (D) Neither displacement nor distance are vectors. (E) Displacement and distance are always equal. 1. Which of the following is the best statement for a velocity? (A) 60 miles per hour (B) 30 meters per second (C) 30 km at 45 north of east (D) 40 km/hr (E) 50 km/hr southwest 13. A jogger runs 4 km in 0.4 hr, then 8 km in 0.8 hr. What is the average speed of the jogger? (A) 10 km/hr (B) 3 km/hr (C) 1 km/hr (D) 0.1 km/hr (E) 100 km/hr 14. A motorcycle starts from rest and accelerates to a speed of 0 m/s in a time of 8 s. What is the motorcycle s average acceleration? (A) 160 m/s (B) 80 m/s (C) 8 m/s (D).5 m/s (E) 0.4 m/s AP Physics 1 Page 0

21 15. A bus starting from a speed of +4 m/s slows to 6 m/s in a time of 3 s. The average acceleration of the bus is (A) m/s (B) 4 m/s (C) 6 m/s (D) m/s (E) 6 m/s 16. A train accelerates from rest with an acceleration of 4 m/s for a time of 0 s. What is the train s speed at the end of 0 s? (A) 0.5 m/s (B) 4 m/s (C).5 m/s (D) 0.8 m/s (E) 80 m/s 17. A football player starts from rest 10 meters from the goal line and accelerates away from the goal line at 5 m/s. How far from the goal line is the player after 4 s? (A) 6 m (B) 30 m (C) 40 m (D) 50 m (E) 60 m 18. A ball is dropped from rest. What is the acceleration of the ball immediately after it is dropped? (A) zero (B) 5 m/s (C) 10 m/s (D) 0 m/s (E) 30 m/s AP Physics 1 Page 1

22 Questions 19 1: A ball is thrown straight upward with a speed of +1 m/s. 19. What is the ball s acceleration just after it is thrown? (A) zero (B) 10 m/s upward (C) 10 m/s downward (D) 1 m/s upward (E) 1 m/s downward 0. How much time does it take for the ball to rise to its maximum height? (A) 4 s (B) 1 s (C) 10 s (D) s (E) 1. s 1. What is the approximate maximum height the ball reaches? (A) 4 m (B) 17 m (C) 1 m (D) 7 m (E) 5 m AP Physics 1 Page

23 . Which two of the following pairs of graphs are equivalent? (A) x v t 0 t (B) x v t 0 t (C) x t v 0 t (D) x v t 0 t (E) x t v 0 t Questions 3 4: Consider the velocity vs time graph below: 3. A which time(s) is the object at rest? (A) zero (B) 1 s (C) 3 s to 4 s (D) 4 s only (E) 8 s 4. During which interval is the speed of the object decreasing? (A) 0 to 1 s (B) 1 s to 3 s (C) 3 s to 4 s (D) 4 s to 8 s (E) the speed of the object is never decreasing in this graph AP Physics 1 Page 3

24 Part II. Free Response Questions Read each question carefully and answer all parts. You may use a separate sheet of paper if you need more space. 1. A displacement is a length with a particular direction, and therefore can be represented by a vector. An explorer travels a displacement of 0 km at an angle of 30 from east, then 30 km at 45 from east, then 0 km 10 from east, and finally, 10 km at 40 from east. Label each of these displacement vectors A, B, C, and D, respectively. All angles are measured counterclockwise from the east axis. (a) Determine the total distance traveled by the explorer in meters. (b) Choose a scale, and using a protractor and a ruler, add the displacement vectors head-to-tail on the graph provided below. Be sure to clearly label each vector. Scale Title: (c) What is the resultant displacement of the explorer from his original starting point? Be sure to indicate both the magnitude of the resultant displacement and its direction from east. Resultant AP Physics 1 Page 4

25 (d) Using the sine, cosine, and/or tangent of the appropriate angles, find the x- and y- components of each of the displacement vectors. (e) Using addition of vectors by means of components, find the magnitude and direction of the resultant vector. AP Physics 1 Page 5

26 . A cart on a long horizontal track can move with negligible friction to the left or to the right. During the time intervals when the cart is accelerating, the acceleration is constant. The acceleration during other time intervals is also constant, but may have a different value. Data is taken on the motion of the cart, and recorded in the table below. Displacement x(m) Velocity v(m/s) time t(s) (a) Plot these data points on the v vs t graph below, and draw the best-fit straight lines between each data point, that is, connect each data point to the one before it. The acceleration is constant or zero during each interval listed in the data table. AP Physics 1 Page 6

27 (b) List all of the times between t = 0 and t = 10 s at which the cart is at rest. (c) i. During which time interval is the magnitude of the acceleration of the cart the greatest? ii. What is the value of this maximum acceleration? (d) Find the displacement of the cart from x = 0 at a time of 10 s. (e) On the following graph, sketch the acceleration vs. time graph for the motion of this cart from t = 0 to t = 10 s. AP Physics 1 Page 7

28 3. A whale comes to the surface to breathe and then dives at an angle of 0.0⁰ below the horizontal. If the whale continues in a straight line for 150 m, (a) how deep is it, and (b) how far has it traveled horizontally. (c) Include a diagram and show all of your work. 4. A volcano launches a lava bomb straight upward with an initial speed of 8 m/s. Taking upward to be the positive direction, find the speed and direction of motion of the lava bomb (a).0 seconds and (b) 3.0 seconds after it is launched. Show all calculations and equations used. 5. When a chameleon captures an insect, its tongue can extend 16 cm in 0.10 seconds. (a) Find the magnitude of the tongue s acceleration, assuming it to be constant. (b) In the first s, does the tongue extend 8.0 cm, more than 8.0 cm, or less than 8.0 cm? Support your conclusion with a calculation. 6. You are driving through town at 1.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and begin decelerating at 3.5 m/s. (a) How far do you travel before stopping? (b) When you have traveled only half the distance in part (a) is your speed 6.0 m/s, greater than 6.0 m/s, or less than 6.0 m/s? Support your answer with a calculation. AP Physics 1 Page 8

29 7. A toy car with essentially frictionless wheels is to be released at the top of an inclined plane such that it will accelerate down the ramp until it reaches the bottom, after which it will continue to roll along the floor. You have been given the assignment of developing an experimental procedure and data tables that will allow you to measure the car s experimental acceleration on the ramp and its velocity on the floor. Please answer the following questions on a separate sheet of paper (or type it) using complete sentences.. (a) What materials commonly found in a science lab or classroom would you need to conduct this experiment? Explain what you would use each piece of equipment for. (Note that you do not have access to computers or computer-based measuring devices such as motion detectors, smart pulleys, or other probeware.).. (b) What experimental procedure would you use to measure the car s acceleration down the ramp, and velocity along the floor? Describe your procedures as a series of ordered steps, use the diagram to identify what measurements you would make, and identify which equipment from part (a) you would use in your data collection... (c) Create appropriate data table(s) with clearly-labeled headers that you would use to record the data from your experiment.. (d) Clearly describe how you will analyze the data you have collected for each part of the experiment (ramp and horizontal surface). AP Physics 1 Page 9