Kinematics - Worksheets

Transcription

1 Worksheet 1 Measurement & Calculations k) l 1. Find the value of the measurements taken from the scales below. a) b) l) m) c) d) 2. Draw pictures of the scales from which the following measurements were taken. e) f) a) 3.2 x 10 2 g b) s c) 32.7 ml d) 2.2 x 10 3 kg e) 1 x 10 2 cm f) 205 ml g) 1.2 x 10 3 kg h) 7.39 s 3. Carry out the following operations using scientific notation. a) 6800 ml x ml b) g x L c) L x 250 L/s d) 3.2 x 10 7 m / m/s e) 1 x 10 6 s x L/s f) L x 20 g) h) g) g h) km cm L i) kg j) mol h 4. Carry out the following operations using scientific notation. a) ( m)( 140 m/s) s 2 i) j) b) (4200 g) 2 x L 0.35 s x m c) 300 kl kl 6000 h x 200 m d) (0.024 m)( m/s)( kg) 2 (0.005 kg)(6000 L)( s) e) ( m x kg) 2 x 200 ml ml x ml/s 1

2 f) L x 10 3 L Explain the difference between precision and accuracy using an example 6. For the left hand column tell how many significant digits are in each number and for the right hand side round to the number of significant digits required. #significant digits (round for) a) m g) cm3 (2) b) 130 g h) g (3) c) cm i) g (3) d) m j) cm (1) e) 0.12 km k) L (5) f) ml l) um (4) 7. Perform the indicated operations. a) Add b) Add 7.32 g L 13.9 g 3.21 L g L c) Add d) Subtract s ml s ml 3. There is no difference between the unit symbol for singular and plural. kg not kgs) 4. The symbol cc must not be used to replace ml or cm Metre and litre are spelled with re (Meter refers to a measuring instrument and not a length.) 6. Kilometre should be pronounced the same way as in kilogram, kilolitre and kilowatt. The term kilo should not be used to refer to a kilogram nor should klick be used to refer to a kilometre. (kilo-metre not kil-aumetre) 7. The term mass should be used not weight when referring to metric masses. (i.e. The mass of the boy is 56 kg.) 8. A specific temperature and a temperature change both have units of degrees Celsius ( o C). 9. Use the unit symbol in preference to words following a numerical value. (e.g g/ml not 10.0 grams per millilitre.). If the amount is written out, then words should be used (e.g., ten grams per millilitre). e) Multiply ( 27.3 g/ml )( 1.2 ml ) = f) Multiply m x 1 km = 1000 m 8. Perform the following operations using your calculator. Answer with scientific notation and significant digits. a) (3.4 x10 8 m/s) 3 ( s) b) ( cm cm 3 ) 2/3 ( g ) SI unit and symbol metre m c) (3( )( ) 4 ) 3/2 tonne t 24 mole mol d) ( )( ) g litre L ( )( ) g/l second s The SI Metric system day d hour h 1. Unit symbols are lower case letters (unless named after a year a person; e.g. C, and Pa). An exception is the use of L for litres. Ampere A Volt V The names of units are always in lower case letters, e.g. grams Coulomb C not Grams, with one exception being degrees Celsius. Joule J 2. A period should not follow the unit symbol.( kg not kg.) 10. For values less than one, use a zero in front of the decimal point; i.e., g not.0695 g. 11. Use a space (not a comma) to separate sets of three digits to the left and the right of the decimal point. The practice is optional where there are only four digits to the left or right of the decimal point. Use decimal fractions (0.5) rather than common fractions (1/2) when working with metric units. kilowatt hour Pascal kw. h Pa 2

3 prefix symbol factor exa E peta P tera T giga G 10 9 * mega M 10 6 * kilo k 10 3 hecto h 10 2 deca da 10 1 SI base unit (m for example) 10 0 deci d 10-1 *centi c 10-2 *milli m 10-3 * micro u 10-6 nano n 10-9 pico p femto f atto at ) Metric Conversions: a) 992 ml = L b) mm = m c) 12 ms = s d) 11.2 m = mm e) kg = g f) km = cm g) 1.00 a = s h) 5120 m/s = km/h i) 3456 ML = GL j) 7.28 x 10 5 mg = kg k) 2.54 cm 2 = mm 2 l) GL = ml m) 0.34 m 3 = cm 3 n) 1.25 L H2O = g o) cm = pm p) 47 m/s = km/h q) 4.00 x g = kg r) ml/s = L/h s) kg/m 3 = g/cm 3 t) 3.00 x 10 8 m/s = km/a u) 3.2 x 10 4 t/h = kg/s 11) Find the SI error(s) in each of the following statements and make the correction(s). a) Officer Martin estimated Greg's velocity as 80 to 90 klicks through the school zone. b) To obtain an exact concentration of.0035 mole per liter a weight of grams of NaOH is dissolved in 100,000 c.c. of solution. c) Sam used his micrometre to determine the bore of the.035 gm. widget to be 56 millimetres. d) The boiling point of water is 212 degrees fahrenheit. The difference between the melting point (32 F) and the boiling point is 280 degrees. 12 Find the SI error(s) in each of the following statements and make the correction(s). a) Nancy bought 3.50 kilos of stewing beef from the butcher. b) The pancake recipe called for 1.0 ML of vanilla extract and 150 c.c. of milk. c) Andrew bought 15.2 liters of gasoline for his 750 c.c. motorcycle. d) Sally's temperature dropped by.8 c (from 39.2 celsius to 38.4 degrees centigrade) in 12 hrs e) The car accelerated from rest to 150 Km per hour in 10 sec. 13 Isolate the indicated variable in each of the following equations: a) F = BIL ; I b) mag c) = xd nl ; d d) e) F = 4 mr cent ; m 2 f) T g) a = v 2 h) R ; v F = Gm m grav R i) d = ( v i + v f ) t ; vf j) 2 k) E = kq 1 p l) R ; q v f = v i + at ; t d = v t at 2 i ; a d = ( v i + vf )t ; t 2 E = k 1 2 ; m 2 1 c - W ; c F mag = qv ; q m) T = 2 m n) k ; m v 2 = v 2 f i + 2ad ; a 3

4 Worksheet 2 - Conventions of Direction - Tables 1. What signs would you give to initial position, initial velocity and acceleration for a ball thrown upwards from the top of a tall building? 2. Label the initial position, velocity and acceleration as positive or negative using the conventions of direction. a) b) m/s east is accelerated at a constant rate of +2.0 m/s 2 i) What is the distance that the object covers during its motion? ii) What does it mean to have negative displacement? 8) Construct a P-V-T table, for 6 s at 1 s intervals, for each of the motions described below. Then, answer the questions below each table. a) An object with initial velocity of +5 m/s is accelerated at a constant rate of 2.0 m/s 2 from a position a position 10 m to the east i) What is the average velocity of the object? ii) What does it mean to have a negative acceleration? 3. What signs would you give to position, initial velocity and acceleration for a helium filled balloon released by a woman in a roller coaster cart going downhill? 4. Draw a diagram for the situations described and decide whether the vector values of initial position, velocity and acceleration should have positive or negative values a) A man in a rising balloon releases a ball. b) An object 35 m east is moving towards you and slowing down. c) An object 20 m west is moving away from you and speeding up d) An object is dropped from a cliff. 5. Construct a P-V-T table, for 6 s at 1 s intervals, describing a ball that starts out 20.0 m to the east of the observer and comes towards the observer at a constant velocity of 3.5 m/s: 6. Construct a P-V-T table, for 6 s at 1 s intervals, P-V-T table describing a ball that rolls across a floor to the west at a constant velocity of 5.0 m/s, starting from a position 2.00 m west of the observer. 7) Construct a P-V-T table, for 6 s at 1 s intervals, for each of the motions described below. Then, answer the questions below each table. a) an object with initial velocity of + 10 m/s is accelerated at a constant rate of -1.5 m/s 2 from a position a position 45 m to the east i) What is the average velocity of the object? ii) What does it mean to have a negative acceleration? b) an object which starts out 10 m to the west traveling at 6 b) An object which starts out 10 m to the west traveling at 6 m/s east is accelerated at a constant rate of +3.0 m/s 2 i) What is the distance that the object covers during its motion? ii) What does it mean to have a negative position? 9. Construct a P-V-T table, for 6 s at 1 s intervals, for an object accelerating at 5.5 m/s 2 from a position 3.0 m to the west with an initial velocity of 2.0 m/s east. 10. Construct a position, velocity, time table describing the first six seconds of the motion of an object that starts out at a distance of 280 m to the west of an observer traveling at 32.0 m/s towards the observer and accelerating towards the observer with a uniform acceleration of 3.5 m/s Construct a position, velocity, time table, for the first twelve seconds, at 2 s intervals, describing the motion of an object that starts out at a distance of 55 m to the east of an observer traveling at 5.0 m/s towards the observer and accelerates towards the observer with a uniform acceleration of 2.5 m/s Construct a position, velocity, time table for every third second for an object accelerating at 1.5 m/s 2 from a position 20 m to the east with an initial velocity of 15.0 m/s west. Make your table for the first fifteen seconds. Worksheet 3: Kinematics Word Problems 1.If you are driving a truck at 90.0 km/h and look to the side for 2.0 s, how far do you travel during this inattentive period? (50 m) 2. In a T.V. picture tube electrons travel from the picture tube projection gun to the screen a distance of about 45 cm in s. What is their velocity in km/h? (3 x 10 2 km/h) 4

5 3. How long does it take a car traveling at 120 km/h 9.40 s, from a standing start, what is his acceleration? to travel 1100 m (33.0 s) (0.640 m/s 2 ) 4. If a speed boat travels 3.4 km while accelerating from 15.0 m/s to 35.0 m/s in a given period of time, what is the average velocity of the boat?) (25.0 m/s) 5. An airplane reaches an air speed of 640 km/h after accelerating. If the plane's average velocity was 164 m/s, what was the initial velocity of the plane? 541 km/h) 6. A sailboat requires 8.00 min to accelerate from 18 km/h to its final velocity. If the average velocity of the motion is 24.0 km/h, what is the final velocity? (8.3 m/s) 7. A car needs a speed of 40.0 m/s at the bottom of a ramp to make a jump from one ramp to another. If it takes 12.0 s for this car to reach 40.0 m/s, what is the displacement from the bottom of the ramp if the car be started from rest? (240 m) 11. An arrow travels a displacement of 355 m in 11.5 s. It strikes a target at 25.0 m/s. What was the initial velocity of the arrow? (36.7 m/s) 12. A spacecraft has a velocity of 150 m/s. If it accelerates over a displacement of 2.5 km in a 15.0 s period, what is the final velocity of the craft? (1.8 x 10 2 m/s) 13. A car accelerates over a distance of 3.0 x 10 2 m from rest to a velocity of 45.0 m/s. What time is required to achieve this velocity? (13 s) 14. A car accelerates over a distance of 4.0 x 10 2 m from 7.50 m/s to a velocity of 37.0 m/s. What time does the car require to reach this velocity? (18 s) 15. An airplane is traveling at 500 km/h. If the pilot accelerates at 20 km/h 2 for 4.0 h how fast will he be traveling at the end of this time? (580 km/h) 16. A circular track is 1500 m in diameter. A car makes 5.00 laps around the track in 8.9 min. Calculate the average speed in km/h. Remember C = 2 r (1.6 x 10 2 km/h) 17. A ball is thrown down from a tower and 3.50 s later is traveling at 50.0 m/s. With what velocity was the ball thrown? (15.7 m/s) 18. If a runner reaches a speed of 6.02 m/s after 19. An arrow is shot straight up with an initial velocity of 45.0 m/s. If 3.7 s later its speed is 8.62 m/s upwards. At what rate is the arrow decelerated by the pull of the earth's gravitational field? (-9.8 m/s 2 ) 20. If a car decelerates at a rate of 6.00 m/s 2 on wet pavement how long will it take the car to come to a complete stop if it is originally traveling at 120 km/h on a wet highway? (5.56 s) 21. A swimmer diving from a bridge requires 1.50 s to reach the water. How high is the bridge? (11.0 m) 22. A skidoo accelerates at m/s 2 over a distance of 300 m in 22.5 s. What was the initial velocity of the skidoo? (9.96 m/s) 23. A 'hot wheels' car accelerates at m/s 2 over a displacement of 5.00 m in 6.7 s. What was the starting velocity of the car? (0.66 m/s) 24. A bus is traveling at 65.0 km/h when it begins to accelerate. If the bus covers a displacement of 4.50 km in the next 4.02 min, what is the rate of acceleration? (4.98 x 10-3 m/s 2 ) 25. How long does it take a crate to fall from the top of a 40.0 m tall grain elevator to the ground below? (2.86 s) 23. A plane travels a distance of 550 m while being accelerated uniformly from rest at the rate of 4.5 m/s 2. What final speed does it attain? (70 m/s) 24. A steel hook carrying a line is to be thrown to the top of a cliff 10.0 m high. Calculate the lowest speed at which the hook could leave the thrower's hand to just reach the top of the cliff. (14.0 m/s) 25. A jet plane starting from rest undergoes an acceleration of m/s 2 straight down the runway for a displacement of m. Calculate the take-off speed and the time required to take off. (63.2 s) 26. A box falls from the back of a truck traveling 55.0 km/h and slides along the ground for a displacement of m before coming to rest. Find the acceleration and the time before the box comes to rest. (13.1 s) 5

6 27. A baseball is hit straight upward with a velocity of 39.2 m/s. Find the maximum height reached. (78.3 m) Worksheet 4: Graphing 1. Use the following information of volume recorded for different lengths of pipe to plot a graph. Find the slope of the graph.) Length (m) Mass (g) An experimenter measures the weight (force) of several different lengths of metallic wire. Length (cm) Force (N) Draw a graph of the following information which was gathered by finding the rate of chemical reactions (time) for different concentrations of reactant A. Concen (mol/l) Time (s) Graph the following using the information given. The position of an object traveling down an inclined surface, from rest, for different times: Position (m) Time (s) Find the slope of each of the graphs below a) 3. Graph the following data collected when an experimenter measured the amount of oil (volume) that could flow through a pipe line at various temperatures. Find the slope of the graph Volume (m 3 /min) Temp ( o C) b) 6

7 7. What is the instantaneous acceleration of the object whose motion is depicted in the figure at a time of 1.58 s? Graphing: Position Velocity Time Graphs Uniform motion: An object moves from a position 4.0 m to the west of an observer at a velocity of +4.0 m/s The slope of a velocity time graph is acceleration (m/s/s = m/s 2 ) The area between the graph line and the x axis is the displacement Area = l x w = v at = Displacement Uniform motion has a slope of zero on a velocity time graph. Position (m) Velocity (m/s) Time (s) The slope of an acceleration time graph has no special meaning (m/s 3 = rate of change of a) For uniform motion, the graph will always be a horizontal line on the x axis a) State all of the motion characteristics for the graph shown below. The slope of a position time graph is velocity Uniform motion has a constant slope: positive if to the east and negative if to the west. 7

8 b) Draw a position time graph for an object starting at 6.0 m east and traveling at +2.0 m/s. Accelerated Motion: An object, starting at a position 6.0 m east of an observer moving at 10.0 m/s west and accelerates at +2.0 m/s 2 east The slope of a velocity time graph is acceleration (m/s/s = m/s 2 ) The area between the graph line and the x axis is the displacement Area = l x w = ((v I + v f)/2)t = D Accelerated motion has a positive slope when acceleration is positive and a negative slope when acceleration is negative. Position (m) Velocity (m/s) Time (s) The slope of an acceleration time graph has no special meaning (m/s 3 ) For accelerated motion, the graph will always be a horizontal line with the value of the uniform acceleration. a) Find all the characteristics of the motion shown below. (x i. x f, d,v a, v i, v f, a) The slope of a position time graph is velocity (m/s) Accelerated motion has a changing slope: always curved To find the velocity at 3.0 s, draw a tangent to the curve at the time 3.0 s and find the slope of the tangent. The slope of the secant between 2 points is the average velocity between those 2 times. 8

9 b) Draw the velocity time graph of a ball thrown upward at 20.0 m/s. What is the displacement after 3.0 s? Worksheet 5 - Position Time and Velocity Time Graphs 1) For each of the following graphs determine the values described. a) Find the values of initial position (x i), final position (x f) displacement (d), average velocity (v a), and acceleration (a). b) Find the values of initial position (x i), final position (x f) displacement (d), and instantaneous velocity (v) at 3.0 s. d) Find the values of initial position (x i), final position (x f), displacement (d), distance (d), average velocity (v a), and instantaneous velocity at t = 60 s e) Find the values of initial velocity (v i), final velocity (v f) displacement (d) for the first 10 s, average velocity (v a), and acceleration (a) at 5.0 s. c) Find the values of initial position (x i), final position (x f) displacement (d), average velocity (v a), and instantaneous velocity at t = 50 s. f) Find the values of initial velocity (v i), final velocity (v f ) average velocity (v a), displacement (d) for the time period and instantaneous acceleration (a) at 30 s. 9

10 g) Find the values of initial velocity (v i), final velocity (v f) displacement (d) for the first 20 s, average velocity (v a), and instantaneous acceleration at t = 70 s. Worksheet 6 Interpreting Graphs 1. Careful analysis of a stroboscopic photograph of a moving object yielded information which was plotted on the graph below h) Find the values of initial velocity (v i), final velocity (v f ) average velocity (v a), displacement over the interval shown, and instantaneous acceleration (a) at 30 s. Give the time periods for the following questions a) For what time period was the velocity the greatest? b) What was the greatest velocity? c) When was the velocity the least? d) What was the least velocity? e) What distance did the object move from t = 8 to t = 9.5? f) What was displacement of the object move over the 12 s? 2) Given the following velocity-time graph for an object moving along a line, determine: the acceleration of the object, the displacement from time t = 4.0 s to t = 12.0 s and the velocity at time 6.0 s. 10

11 2. The graph shows the position from the starting point as a function of time for an object in motion. e) f) Position (m) Position as a function of Time Time (s) a) What was the velocity during the first two seconds of motion? b) What was the instantaneous velocity at time 3.0 s? c) Describe the motion. g) h) 4. At t = 0, a sports car traveling at a constant rate passes a stationary motorcycle. This occurs on a straight highway. Their subsequent velocities are shown in a velocity-time graph. Use the graph to solve the following problems. 3. Explain what happens to the traveling object whose motion is depicted by the following graphs. Assume that the initial positions are positive. a) b) c) d) a) Prove or disprove the statement that the motorcycle overtakes the sports car when t = 80 s. b) Determine the average velocity at which the motorcycle travels during this 80 s time interval. c) Approximate the acceleration of the sports car when t = 30 s. 11

12 5. The graph describes the motion of a golf ball fired vertically upward. The golf ball then fell freely after reaching its highest point and bounced upon striking the ground) Worksheet 7 - Using Graphing Calculators a) At what time did the ball reach its maximal height? b) What height did the ball reach? c) At what time did the ball first bounce? d) Why are the lines parallel? 6. At t = 0, a stationary police car is passed by a speeding sports car. This occurs on a straight highway. Their subsequent velocities are shown in a velocity-time graph. 1) Using your graphing calculator, draw a sketch of the graph Time (s) Position (m) a) What is the position of the object after 7.80 s? b) What is the velocity of the object at time t = 9.00 s? c) What is the displacement from time t= 7.80 to t = 9.80 s? d) What is the acceleration of the object? 2) Using your graphing calculator, draw a sketch of the graph a) Prove the police car overtakes the sports car when t = 60 s. b) Determine the average velocity at which the police car travels during this 60 s time interval. c) Find the distance between the two cars when t = 30 s. d) Find the acceleration of the sports car when t = 30 s 7. Here is the velocity-time graph of two cars A and B. At t = 0 s A passed B a) Determine the acceleration of B during the first 2.0 s. b) Find the average velocity of A in the first 8.0 s. c) Find the distance between A and B at t = 4.0 s d) Find the instantaneous acceleration of B at 3.0 s Time (s) Position (m) a) What is the position of the object after 3.50 s? b) What is the velocity of the object at time t = 5.20 s? c) What is the displacement of the object from time t= 2.50 to t = 6.70 s? d) What is the acceleration of the object? 12

13 3) Using your graphing calculator, draw a sketch of the graph Time (s) Position (m) a) What is the position of the object after 3.80 s? b) What is the velocity of the object at time t = 7.12 s? c) What is the displacement of the object from time t= 2.50 to t = 7.80 s? d) What is the acceleration of the object? 4) Using your graphing calculator, draw a sketch of the graph Time (s) Position (m) a) What is the position of the object after 3.39 s? b) What is the velocity of the object at t = 10.2 s? c) What is the displacement of the object from time t= 5.00 to t = 9.50 s? d) What is the acceleration of the object? 5) Using your graphing calculator, draw a sketch of the graph 6) Using your graphing calculator, draw a sketch of the graph Time (s) Velocity (m/s) a) What is the velocity of the object after 2.75 s? b) What is the displacement of the object from time t = 3.50 s to t = 5.50 s? c) What is the acceleration of the object? d) If the object starts at 25 m to the east of the observer, what is its position after 7.50 s? 7) Using your graphing calculator, draw a sketch of the graph Time (s) Velocity (m/s) a) What is the velocity of the object after 2.75 s? b) What is the displacement of the object from time t = 3.50 s to t = 5.50 s? c) What is the acceleration of the object? d) If the object starts at 45.0 m to the west of the observer, what is its position after 3.00 s? 8) Using your graphing calculator, draw a sketch of the graph Time (s) Velocity (m/s) a) What is the velocity of the object after 2.20 s? b) What is the displacement of the object from time t = 3.55 s to t = 4.90 s? c) What is the acceleration of the object? d) If the object starts at 15.0 m to the west of the observer, what is its position after 5.50 s? Time (s) Velocity (m/s) a) What is the velocity of the object after 7.50 s? b) What is the displacement of the object from time t = 1.30 s to t = 6.90 s? c) What is the acceleration of the object? 13

14 d) If the object starts at 36.0 m to the west of the observer, what is its position after 2.50 s? Worksheet 8 - Changing Graphs P-T to V-T and V-T to P-T Time Period Slope = m/s Velocity for the Period 1. Change the following velocity - time graph into a positiontime graph. Assume that the object starts at the observer's position. Time Period Displacement Formula Displacement (m) Position (m) 3) How is an acceleration as a function of time graph converted into a velocity as a function of time graph? 4) How is a velocity as a function of time graph converted into an acceleration as a function of time graph? 2. Using the position-time graph, at left, sketch a velocitytime graph for the same information. Position as Function of Time 14