Unit-3. Force & Motion. Solutions 3.1 Motion in One Dimension page Distance is the scalar and displacement is the vector.

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Terence Porter
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1 3.1 in One Dimension page Which of the following statements about distance and/or displacement are TRUE? Distance is a vector quantity and displacement is a scalar quantity. A person makes a round-trip journey, finishing where she started. The displacement for the trip is zero and the distance is some nonzero value. A person starts at position A and finishes at position B. The distance for the trip is the length of the segment measured from A to B. If a person walks in a straight line and never changes direction, then the distance and the displacement will have exactly the same magnitude. The phrase 20 km, northwest likely describes the distance for a motion. The phrase 20 km, west likely describes the displacement for a motion. Distance is the scalar and displacement is the vector. Displacement is the change in position of an object. An object which finishes where it started is not displaced; it is at the same place as it started and as such has a zero displacement. On the other hand, the distance is the amount of ground which is covered. And if it was truly a journey, then there is definitely a distance. This would only be the case if the person walk along a beeline path from A to B. But if the person makes a turn and veers left, then right and then..., then the person has a distance which is greater than the length of the path from A to B. Distance refers to the amount of ground which is covered. If a person never changes direction and maintains the same heading away from the initial position, then every step contributes to a change in position in the same original direction. A 1 m step will increase the displacement (read as out of place-ness) by 1 meter and contribute one more meter to the total distance which is walked. Distance is a scalar and is ignorant of direction. The "northwest" on this quantity would lead one to believe that this is a displacement (a vector quantity) rather than a distance. The unit is an appropriate displacement unit (length units) and the direction is stated. Since there is both magnitude and direction expressed, one would believe that this is likely a displacement.

2 3.1 in One Dimension page Which of the following statements about speed and/or velocity are TRUE? Velocity is a vector quantity and speed is a scalar quantity. Both speed and velocity refer to how fast an object is moving. The velocity of an object refers to the rate at which the object s position changes. For any given motion, it is possible that an object could move very fast yet have an abnormally small velocity. Speed is a scalar and velocity is the vector. Know this one! Speed refers to how fast an object is moving; but velocity refers to the rate at which one's motion puts an object away from its original position. A person can move very fast (and thus have a large speed); but if every other step leads in opposite directions, then that person would not have a large velocity. That is exactly the definition of velocity - the rate at which velocity changes. An Indy Race car driver is a good example of this. Such a driver is obviously moving very fast but by the end of the race the average velocity is essentially 0 m/s. The average velocity of an object on a round-trip journey would be zero. For a round trip journey, there is no ultimate change in position. As such, the average velocity is 0 m/t seconds. Regardless of the time, the average velocity will be 0 m/s.

3 3.1 in One Dimension page Yes it is. Acceleration is direction-conscious. 3. Which of the following statements about acceleration are TRUE? Acceleration is a vector quantity. Accelerating objects must be changing their speed. Accelerating objects must be changing their velocity. Accelerating objects could be changing their speed; but it is also possible that an accelerating object is only changing its direction while maintaining a constant speed. The race car drivers at Indy might fit into this category (at least for certain periods of the race). Accelerating object MUST be changing their velocity -either the magnitude or the direction of the velocity. Acceleration units include the following; m/s 2, cm/s 2, km/h 2. The direction of the acceleration vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down. An object which is slowing down has an acceleration. The first three sets of units are acceleration units - they include a velocity unit divided by a time unit. The last set of units is a velocity unit divided by a length unit. This is definitely NOT an acceleration. This is the case and something important to remember. Consider its application in the last three parts of this question. Accelerating objects are either slowing down, speeding up or changing directions.

4 3.1 in One Dimension page An object which is moving at constant speed in a circle has an acceleration. Acceleration is the rate at which the velocity changes. To move in a circle is to change one's direction. As such, there is a change in the velocity (not magnitude, but the direction part); this constitutes an acceleration. This is the very definition of acceleration. Know this one - its the beginning point of all our thoughts about acceleration. An object that is accelerating is moving fast. An object that is accelerating will eventually (if given enough time) be moving fast. An object that is moving rightward has a rightward acceleration. Accelerating objects are not necessarily moving fast; they are merely changing how fast they are moving (or the direction they are moving). If the accelerating object is slowing down, then it will eventually stop and not reach a fast speed. And if that doesn't convince you, then consider an object that is accelerating by moving in a circle at constant speed forever; it will accelerate the entire time but never being going any faster than at the beginning. An object that is moving rightward and speeding up has a rightward acceleration. An object that is moving upwards and slowing down has an upwards acceleration. If an object is moving rightward and slowing down, then it would have a leftward acceleration. If an object is speeding up, then the direction of the acceleration vector is in the direction which the object is moving. If an object is slowing down, then the acceleration vector is directed opposite the direction of the motion; in this case the acceleration is directed downwards.

5 3.1 in One Dimension page cm 4. An ant starts from point A and reaches point D in 10 seconds by tracing the path given in the figure. (Each side of the squares is 1 cm.) 5 cm 4 cm 3 cm a) What is the average speed of the ant in cm/s? b) What is the magnitude of average velocity of the ant in cm/s? a) d total =6+4+3= 13 cm s average = d total t b) = = 1,3 cm / s Δ x = 5 cm v average = Δ x t = 5 =0,5 cm / s 10

6 3.1 in One Dimension page A ladybug moves on the grass of a park. She starts to move from point A, first goes to point B and finally reaches point C. The total time for this trip is 100 seconds. 5 m x Answer the following questions according to this information. a) d total = 4+5 = 9 m b) Δ x total =3 m due east a) The distance covered by the ladybug is m. b) The displacement of the ladybug is m. c) s average = d total t = = 0,09 m / s c) The average speed of the ladybug is m/s. d) The average velocity of the ladybug is m/s. d) v average = Δ x total t = = 0,03 m / s due east

7 3.1 in One Dimension page x car = v car.t 6. A car and a motorcycle pass through points K and L at t=0. ( )= 30.t t = = 15 s If car catches motorcycle at point M, what is the speed of the motor in m/s? x motor = v motor.t 300= v motor.15 v motor = = 20 m / s

8 Unit-3 the ant in rage velocity and finally reaches point C. The total time for this constant speeds. Their initial positions (at t=0 ) 5. trip is 100 seconds. are given in the figure. Car B reaches line XY A ladybug moves on the grass of a park. She before car C, after car A. starts to move from point A, first goes to point B and finally reaches point C. The total time for this 3.1 in One Dimension 5. trip is 100 seconds. A ladybug moves on the grass of a park. She page starts to move from point A, first goes to point B 7. and finally reaches point C. The total time for this Carstrip A, Bisand C are moving on a highway at 100 seconds. Classify each statement given below as than the The distance traveled by car A is greater constant speeds. Their initial positions (at t=0 ) absolutely correct, besame correct distance traveled by car might B in the timeorinterval. are given in the figure. Car B reaches line XY wrong. before car C, after car A. So, the speed of car A is greater than the speed of car B. Classify each statement given below as a) The speedcorrect, of car A is greater the or absolutely might bethan correct speed of car B. wrong. a park. She oes to point B tal time for this Answer the following questions according to this information. a) The distance covered by the ladybug is m. Answer the following questions according to this b) information. The displacement of the ladybug is Classify each statement given below as m. be correct or absolutely correct, might a) The distance covered by the wrong. s according to adybug is bug is ybug is dybug is ladybug is Answer following according to m. speedquestions c) The the average of the ladybug is this information. m/s. a) The speed of car A is greater than the b) The displacement of the ladybug is speed of car B. a) d) The distance the ladybug ladybugisis m. covered The average velocity by of the This statement is... m. m/s. c) The average speed of the ladybug is b) speed The displacement the b) The of car Am/s. is greaterof than theladybug is speed of car C. m. 112 d) The average velocity of the ladybug is th This statement is Physics... 9 Grade Workbook c) The average of the ladybug is m/s.speed m/s. absolutely correct This statement is... Classify each statement given below as absolutely be than correct a) The speedcorrect, of car A might is greater the or wrong. speedtraveled of car B.by car A is equal to the distance The distance b) The speed of car A is greater than the traveled speed by carofbcar butc.car A reaches line XY before car C. This statement is... So, the speed of carofacar is greater than than the speed of car C. a) The speed A is greater the This statement is... speed of car B. b) The speed of car A is greater than the This statement is speed of car C.... c) The speed of car B is greater than the speed of car C. absolutely correct This statement is... b) The speed of A is greater than the This statement is car... speed of car C. Nothing can be said about the speeds of cars B and C. c) The speed of car B is greater than the TheyThis can be equal speed of car B can be greater statement... speed of caroris C.the than the speed of car C. 2 c) The speed of car B is greater than the speed of car C. d) The average velocity of the ladybug is m/s. 112 This statement is... th 9 Grade Physics Workbook This statement is... METU Development Foundation High School c) The speed of car B is greater than the speed of car C. might be correct This statement is... 2 METU Development Foundation High School

The initial positions of the cars are as in Figure-1.

9 3.1 in One Dimension page Two cars A and B are moving around circular tracks of radii r and 3r at constant speeds of v A and v B. The initial positions of the cars are as in Figure-1. After a while their positions are as in Figure-2 for the first time. car A; d A = v A.t 3 4.2πr = v A.t car B; d B = v B.t 1 4.2π.3r = v B.t What is the ratio of the speed of car A to the speed of car B, (v A /v B )? 3 4.2πr = v.t A 1 4.2π.3r = v.t B v A v B = 1

10 Unit-3 What is the ratio of the speed of car A to the speed of car B, (va/vb)? 9. What is the ratio of the speed of car A to the Cars A,of B car andb, C (v are/vmoving on a highway at speed A B)? constant speeds. Their initial positions are given What is t in seconds? in the figure. After a while they meet at line XY. Force 11. & Cars A a 5What m/s an is figure. T 3.1 in One Dimension page Cars A, B and C are moving on a highway at constant speeds. Their initial positions are given in the figure. After a while they meet at line XY. 11. Cars A 9. Cars A, B and C are moving on a highway at 5 m/s a The distance traveled by car B is greater than the constant speeds. Their initial positions are given Classify each statement given below as figure. T Classify each statement given below as absolutely correct, might be correct or distance A might inthey the same time in traveled the figure. by Aftercar a while meet at line XY.interval. absolutely correct, be correct or Calcula So, the speed of car B is wrong. greater than the speed of car A. wrong. a) The speed of car B is greater than the a) The speed of car Bspeed is greater 11. of carthan A. the 11. speedeach of car A. at speeds Cars A and B move toward other statement iscorrect Classifyaseach statement given below as absolutely shown inthis the 5 m/s and vb respectively... This statement is correct, might be correct or figure. They meet at absolutely point K.... wrong. Cars A 5 m/s a figure. T Calcula b) The speed of car A is greater than the speed of car C. the b)a)the Thespeed speedof ofcar carabis isgreater greaterthan than the speed of car C. Classify each statement given below as absolutely correct, might be correct or wrong. a) The speed of car B is greater than the speed of car A. This statement is... b) The speed of car A is greater than the speed of car C. This statement is... speed of car A.This is... The distance traveled bystatement car A and the distance traveledthis bystatement car C in is the time interval cannot This statement is... c)same The speed car Cas is equal to thebe speed of Classify each statement givenof below... car B. compared. absolutely Calcula Calculate the velocity of car B correct, in m/s. might be correct or c) The speed of car C is equal to the speed of wrong. This... b) car TheB.speed of car A statement is greater is than the speed of car a) The speed of C. car B is greater than the This statement is... might be correct speed of car A. This statement is... This statement is9th Grade Physics Workbook c) The speed of car C is equal to the speed of... th car B. 9 Grade Physics Workbook c) The speed of car C is equal to the speed of car B. 9 Grade Physics Workbook This statement is... This statement is... th 3 The speed of car Aby is greater than the the distance The b) distance traveled car B and This statement is... speed of car C. traveled by car C in the same time interval cannot be This statement is compared.... c)th The speed of car C is equal to the speed of car B. 3 might be correct th 113 M M

3.1 in One Dimension page - 113 10. The speeds of a car and a bus are 2v and v respectively.

11 3.1 in One Dimension page The speeds of a car and a bus are 2v and v respectively. When they are moving in the same direction as given in top figure, the time needed for the car to pass the bus completely is 2 s. When they are moving in opposite directions as given in bottom figure, the time needed for the car to pass the bus completely is t. first condition 5x =(2v - v).2 5x = 2v second condition 6x =(2v +v).t 2x = t 5x = 2v 5 2x = t 2 = 2 t What is t in seconds? t =0,8 s

12 3.1 in One Dimension page car A; 11. Cars A and B move toward each other at speeds 5 m/s and v B respectively as shown in the figure. They meet at point K. 200 = 5.t t = 40 s car B; Calculate the velocity of car B in m/s. 100 = v B.40 v B = 2,5 m / s

13 3.1 in One Dimension page After the driver of a car applies the brakes, the tires are locked and the car slows down (decelerates) uniformly. According to the information given above, read the following sentences. Print C if the sentence is correct, otherwise print W for the wrong statement. You have to correct the wrong statements by using appropriate words or phrases. The acceleration of the car is opposite to the direction of motion. The acceleration and the net force on the car are opposite to each other. In each second, the distance travelled by the car is the same. C The acceleration of the car is opposite to the direction of motion. W The acceleration and the net force on the car are opposite to each other. W C in the same direction. In each second, the distance travelled by the car is the same. decreases. In each second, the speed of the car decreases by the same amount. In each second, the speed of the car decreases by the same amount.

3.1 in One Dimension page - 114 The area of velocity versus time graph gives the displacement of

Both cars are at the same position at t=8 s. x A =10.8=80 m x B =-20.

14 3.1 in One Dimension page The area of velocity versus time graph gives the displacement of the car. 13. Velocity-time graph of two cars A and B are given. Both cars are at the same position at t=8 s. x A =10.8=80 m x B =-20.8=-160 m What is the position of car B with respect to car A at t=0? A at t=0 at t=8 s 80 m -160 m + direction B at t=0 The position of car B wrt car A at t=0 is 240 m.

15 3.1 in One Dimension page x=v.t 14. Two cars A and B are at the same position at t=0. Their velocity-time graphs are given. The areas of the velocity-time graphs of car A and B are 3x and "2x respectively. 2x=10.t What is the speed of car A (v) in m/s? 3x=v.t 2x=10.t v=15 m/s

b) The speed of car B is m/s. c) d A =9.

20=80 m distance between them is 100 m d) v

16 3.1 in One Dimension page Position-time graphs of two cars A and B are given. a) s A =90/10=9 m/s b) s B =60/15=4 m/s Fill the following blanks. a) The speed of car A is m/s. b) The speed of car B is m/s. c) d A =9.20=180 m d B =4.20=80 m distance between them is 100 m d) v A =9 m/s c) The distance between the cars at t=20 s is m. e) v B =4 m/s d) The velocity of car A at t=4 s is m/s. e) The velocity of car B at t=7 s is m/s.

17 3.1 in One Dimension page A student had performed an experiment explaining the motion of a toy car. He had collected the data and plotted the position-time graph of the toy car as given in the figure. 6 cm A B C Print the points A, B, C and the initial position (x 0 ) on the following scaled figure. x 0 initial position

interval Answer the following questions.

b) In which time interval(s) object is moving due

c) d) -30 m -30/4=-7,5 m/s d) What is the velocity

18 3.1 in One Dimension page An object is initially moving due east and its position-time graph is given. a) 4 s - 6 s time interval b) 6 s - 12 s time interval Answer the following questions. a) In which time interval object is at rest? b) In which time interval(s) object is moving due west? c) What is the initial position of the object? c) d) -30 m -30/4=-7,5 m/s d) What is the velocity of the object in 6 s 10 s interval? e) What is the average speed of the object 2 s 12 s interval? e) ( )/10=7,5 m/s

19 3.1 in One Dimension page The scene given above is taken from the movie 2 Fast 2 Furious. Police car moves at a constant speed of 20 m/s and Brian O Conner s car moves at a constant speed of 10 m/s. The distance between them is 100 m initially. b) Let s choose the position of Brian O Conner as reference point. Plot position-time graphs and velocity-time graphs of both cars until police car catches the O Conner s car. (Show the lines of police car and O Conner s car on the same graph. Label police car with P and Brian O Conner s car with B.) a) What is the time needed for the police car to catch O Conner s car? 100 =(20-10).t B P 10 t = t = 10 s P B

20 3.1 in One Dimension page suppose that the length of the path is 240 km 80 km 60 km 100 km 19. A car travels one-third of the path with a speed of 40 km/h, one-fourth of the path with a speed of 30 km/h and the remaining part of the path with a speed of 50 km/h. What is the average speed of the car for the whole trip in km/h? A B C D 40 km/h 30 km/h 50 km/h t 1 t 2 t 3 t 1 =80/40=2 h t 2 =60/30=2 h t 3 =100/50=2 h v average =(240)/(2+2+2)=240/6 v average =40 km/h

21 3.1 in One Dimension page A car moves with a constant speed on a circular horizontal path. After 10 seconds, it reaches the starting point. Read the following statements. If the statement is CORRECT, print C, or if it is WRONG then print W. You have to correct the wrong statements by using appropriate word(s) or phrase. C C W Velocity of the car is not constant during the trip. Displacement of the car is zero at the end of 10 seconds. zero. Displacement of the car is equal to total distance travelled. The speed of the car is constant but the direction of motion changes. The car is at its starting point at the end of 10 s. So, its displacement is zero. The displacement of the car is zero.

22 3.1 in One Dimension page A car moves along a straight road at a constant velocity of 30 m/s due north for 20 seconds and stops for 10 seconds and then moves in the opposite direction at a constant velocity of 20 m/s for 20 seconds. x 1 =30.20=600 m a) What is the distance covered by the car at the end of the trip in meters? x 2 =0 a) d= =1000 m b) What is the displacement of the car at the end of the trip in meters? b) x= =200 due north c) What is the average speed of the car in m/s? x 3 =20.20=400 m c) s average =1000/( ) s average =1000/50 s average =20 m/s

23 3.1 in One Dimension page suppose that the length of the path is 240 km v average =30 km/h 80 km 160 km 22. A car travels one-third of its path at 60 km/h and the remaining part of the path at velocity v. The average speed of the car for the whole trip is 30 km/h. Calculate the velocity v in km/h. A B 60 km/h v t 1 t 2 t 1 =80/60=4/3 h t 2 =160/v C 30=(240)/t t=(240)/(30)=8 h 8=(4/3)+(160/v) v=24 km/h

Physics 11 Kinematics Review: Vectors, Displacement, Velocity, Acceleration, & Kinematics Equations

Physics 11 Kinematics Review: Vectors, Displacement, Velocity, Acceleration, & Kinematics Equations Review of Kinematics in 1 Dimension: True or False? Mark each statement as T (true) or F (false). If