Deck 2: Motion in a Straight Line

Question 1

A car moving along the x direction has acceleration,a_x that varies with time as shown in the figure.At the moment,t = 0 s,the car is located at x = 12 m and has a velocity of 6 m/s in the positive x direction.What is the position of the car at t = 4.0 s?

A)76.5 m
B)15.6 m
C)59.5 m
D)21.6 m
E)-3.2 m

Answer 1

59.5 m

Question 2

An Olympic runner starts from rest and accelerates at 2.00 m/s².Assume constant acceleration for the entire time.How far does he travel in 10.0 s?

A)100 m
B)500 m
C)1000 m
D)2000 m

Answer 2

100 m

Question 3

A ball is thrown straight up into the air,it reaches the top of its path and then falls back down to its initial position.During its flight,when is its speed greater than zero? Ignore air resistance.

A)only when it's moving up
B)when it's moving up and when it's moving down
C)never
D)only when it's moving down
E)always

Answer 3

when it's moving up and when it's moving down

Question 4

The position of a nanoparticle as a function of time is x(t)= t² - t - 6,where x is measured in meters,t is measured in seconds and t > 0.What is the minimum value of the nanoparticle's position?

A)6.00 m
B)-6.00 m
C)6.25 m
D)-6.25 m
E)The nanoparticle does not have a minimum value for its position for t>0.

Question 5

A bullet is fired through a board,8.00 cm thick,with its line of motion perpendicular to the face of the board.If it enters with a speed of 300 m/s and emerges with a speed of 100 m/s,the bullet's acceleration as it passes through the board is

A)-200,000 m/s².
B)-300,000 m/s².
C)-400,000 m/s².
D)-500,000 m/s².
E)-600,000 m/s².

Question 6

The position of a nanoparticle as a function of time is x(t)= t² - t - 6,where x is measured in meters,t is measured in seconds and t > 0.When is the speed of the nanoparticle zero?

A)when t = 0.5 s
B)when t = 2 s
C)when t = 3 s
D)The speed of the nanoparticle is never zero.

Question 7

Two girls stand at the edge of a cliff.One girl throws a stone upwards with a velocity of 10.0 m/s and the other throws her stone downwards at 10.0 m/s.If they threw them from the same height at the same time,which stone will have the greatest speed when it hits the ground?

A)The stone that was thrown upward
B)The stone that was thrown downward
C)They will have the same speed.

Question 8

The acceleration of a race car as a function of time is a(t)= kt,where a is measured in meters per second squared,t is measured in seconds and k is a constant.If its velocity at t = 0 is 2 m/s,and it is 26 m/s at t = 2 s,what is the value of the constant,k?

A)12 m/s³
B)12 m/s²
C)24 m/s³
D)24 m/s²
E)13 m/s³

Question 9

The graph of the velocity of a rocket (on the vertical axis)vs.time (on the horizontal axis)is a straight line that does not go through the origin and does not have a slope of zero.Which statement is true?

A)Its position is always zero.
B)Its speed is always zero.
C)Its acceleration is not zero.
D)Its velocity is constant.

Question 10

A ball is thrown straight up into the air,it reaches the top of its path and then falls back down to its initial position.During its flight,when is it accelerating in the downward direction? Ignore air resistance.

A)always
B)when it's moving up
C)never
D)when it's moving down

Question 11

The graph of the position of a DNA molecule (on the vertical axis)vs.time (on the horizontal axis)is a straight line that does not go through the origin and does not have a slope of zero.Which statement is true?

A)Its position is always zero.
B)Its velocity is always zero.
C)Its speed is always zero.
D)Its acceleration is always zero.

Question 12

A fellow student found in the performance data of his new car the velocity-versus-time graph shown in the figure.The average acceleration of his car from second 0 to second 24 is

A)5 m/s².
B)2.5 m/s².
C)0 m/s².
D)-2.5 m/s².
E)-5 m/s².

Question 13

A car moving along the x direction has acceleration,a_x that varies with time as shown in the figure.At the moment,t = 0 s,the car is located at x = 12 m and has a velocity of 6 m/s in the positive x direction.What is the velocity of the car at t = 4.0 s?

A)16 m/s
B)15.6 m/s
C)14.4 m/s
D)0 m/s
E)-12.7 m/s

Question 14

The driver of a car travels 150 miles to reach his destination.If he travels 60.0 mi/h for 100 miles and 55.0 mi/h for the remaining 50.0 miles,what was his average velocity for the trip?

A)57.8 mi/h
B)58.2 mi/h
C)58.7 mi/h
D)59.0 mi/h

Question 15

The driver of a car travels 150 miles to reach his destination.If he travels 60.0 mi/h for 100.0 miles and 55.0 mi/h for the remaining 50.0 miles,how long does it take for him to reach his destination?

A)1.58 hours
B)2.45 hours
C)2.58 hours
D)3.67 hours

Question 16

A car moving along the x direction has acceleration,a_x that varies with time as shown in the figure.At the moment,t = 0 s,the car is located at x = 12 m and has a velocity of 6 m/s in the positive x direction.What is the displacement of the car between t = 1.0 s and t = 2.0 s?

A)-0.8 m
B)5.6 m
C)11.1 m
D)2.8 m
E)9.5 m

Question 17

A car travels north at 30 m/s for 10 minutes.It then travels south at 40 m/s for 20 minutes.The total distance the car has traveled and its displacement are,respectively,

A)66 km and 30 km.
B)30 km and 66 km.
C)51 km and 9 km.
D)9 km and 51 km.
E)51 km and 30 km.

Question 18

The velocity of a car is given as m/s where m/s³, m/s²,and m/s.What is its acceleration at s?

A)15 m/s²
B)18 m/s²
C)20 m/s²
D)32 m/s²

Question 19

If an electron and a proton have the same initial position at the same initial time,and the same final position at the same final time,then which velocity would always be the same for both?

A)initial velocity
B)final velocity
C)average velocity
D)instantaneous velocity

Question 20

The graph of the position of a DNA molecule (on the vertical axis)vs.time (on the horizontal axis)is a straight line that does not go through the origin and does not have a slope of zero.Which statement is true?

A)Its speed is always zero.
B)Its velocity is constant.
C)Its position is always zero.
D)Its acceleration is not zero.

Question 21

A student throws a ball straight up at 22 m/s,releasing the ball 1.5 m above the ground.What is the maximum height of the ball above the ground?

A)24.7 m
B)3.0 m
C)15.3 m
D)26.2 m
E)27.7 m

Question 22

How much runway does a 150,000-kg cargo plane need if it uniformly reaches its minimum takeoff speed of 135 m/s in 12 seconds?

A)1020 m
B)810 m
C)405 m
D)1620 m
E)More information is needed.

Question 23

At time,t = 0 s,car A is at rest at the origin of the coordinate system and car B is moving due East at a constant velocity of 20 m/s.When car B is 50 m west of car A, car A starts to move at a constant acceleration of 2 m/s² due East.A certain time later car B overtakes car A. How far from the origin has car A moved when car A eventually catches up with car B and once again moves farther East of car B?

A)87.2 m
B)218 m
C)291 m
D)108 m

Question 24

A rock is dropped off of a building,reaching a constant speed of 37 m/s after 4 s.What is the rock's acceleration after 5 seconds?

A)9.8 m/s²
B)12.3 m/s²
C)0 m/s²
D)9.3 m/s²
E)4.4 m/s²

Question 25

Two trains,one travelling at 20 m/s and the other at 40 m/s,are headed toward one another along a straight level track.When they are 950 m apart,each engineer sees the other's train and applies the brakes.Assuming both trains have equal magnitude accelerations after the brakes are applied,determine the minimum magnitude of this acceleration in order to avoid a collision.

A)1.62 m/s²
B)0.87 m/s²
C)3.45 m/s²
D)1.05 m/s²
E)2.15 m/s²

Question 26

The figure shows the time dependent velocity of an object.Assuming that the object starts from rest at the origin of the coordinate system,what is the magnitude of the displacement of the object at t = 5 s?

A)75 m
B)55 m
C)60 m
D)40 m
E)85 m

Question 27

In the classic book by Jules Verne,Phileas Fogg travels around the world in 80 days.Leaving London,heading east,and arriving back in London 80 days later from the west.If the radius of the Earth is 6.38 x 10⁶ m (for this problem,treat London as being on the equator),find the average velocity of Mr.Fogg.

A)zero
B)0.92 m/s
C)5.8 m/s
D)More information is needed.

Question 28

A golf ball is dropped from a height of 1.0 m onto a concrete floor.The velocity of the ball immediately before hitting the floor is 4.43 m/s downward.The ball contacts the floor for 0.940 ms (check out R.Cross,Am.J.Phys.,Vol.67,No.3,March 1999)and leaves the floor traveling upward at 3.96 m/s.The average acceleration of the golf ball while it is in contact with the floor is

A)9.81 m/s².
B)8.93 * 10³ m/s².
C)500 m/s².
D)4.71 * 10³ m/s².
E)4.21 * 10³ m/s².

Question 29

A 1050 kg car is traveling at a speed of 25 m/s when the driver sees that there is a tree across the road.If the car has a constant deceleration of -5.0 m/s² and the driver has a reaction time of 0.30 s,how far does the car travel before it comes to a stop?

A)7.5 m
B)8.0 m
C)63 m
D)70 m

Question 30

A ball is dropped from rest from a height h above the ground.Another ball is thrown vertically upwards from the ground at the instant the first ball is released.Determine the initial speed of the second ball if the two balls are to meet at a height h/2 above the ground.

A)h/g
B)
C)
D)g/h
E)

Question 31

A 747 commercial jet liner moves down a runway at a constant acceleration,starting from rest and reaching the take-off speed of 285 km/hr after travelling 3400 m down the runway.The acceleration of the jet on the runway is

A)0.0233 m/s².
B)0.00248 m/s².
C)9.81 m/s².
D)1.84 m/s².
E)0.922 m/s².

Question 32

In the classic book by Jules Verne,Phileas Fogg travels around the world in 80 days.Leaving London,heading east,and arriving back in London 80 days later from the west.If the radius of the Earth is 6.38 x 10⁶ m (for this problem,treat London as being on the equator),find the average speed of Mr.Fogg.

A)zero
B)0.92 m/s
C)5.8 m/s
D)More information is needed.

Question 33

If the position of an object (in meters)is given by the relation ,how fast the object moving at a time of 4.00 s?

A)6.51 m/s
B)20.4 m/s
C)31.6 m/s
D)37.5 m/s
E)150 m/s

Question 34

A heavy ball is dropped into a lake from a height of 30.0 m above the water.It hits the water with a certain velocity and continues to sink to the bottom of the lake at this same constant velocity.It reaches the bottom of the lake 10.0 s after it was dropped.How deep is the lake?

A)182.5 m
B)87.4 m
C)29.6 m
D)143.1 m
E)209.7 m

Question 35

One of the following statements is false.Which one is it?

A)The size of the displacement and the distance travelled can be the same.
B)The size of the displacement and the distance travelled can be different from each other.
C)If a car only travels in a straight line without turning,the size of the displacement and the distance travelled are the same.
D)The size of the displacement can be greater than the distance traveled.
E)The size of the displacement is always less than or equal to the distance traveled.

Question 36

A particle moves in the one direction,stops,and then heads back in the opposite direction.The position of a particle (in meters)as a function of time is given by x(t)= -3.65 t² + 4.52 t + 7.91.The position of the particle where it stops is

A)0 m.
B)9.31 m.
C)11.7 m.
D)-11.7 m.
E)-9.31 m.

Question 37

A person fires a warning shot out of handgun.If the bullet leaves the gun with an initial speed of 305 m/s and travels straight upward,how much time does the person firing the gun have to move out of the way before the bullet hits the ground? (Ignore the effects of air resistance.)

A)15.6 s
B)31.1 s
C)62.2 s
D)None are correct.

Question 38

A stone is thrown downward with an initial velocity of 5.00 m/s.The acceleration of the stone is constant and has the value of the free fall acceleration,9.81 m/s².The speed of the stone after 0.750 s is

A)12.4 m/s.
B)14.9 m/s.
C)22.7 m/s.
D)32.3 m/s.
E)0 m/s.

Question 39

A car takes 60.0 minutes to travel 100 km.During this one-hour trip,the car stops for 5 minutes to get gas.The speed limit on the road that the car traveled on is 100 km/hr.Which of the following statements is true?

A)The car never exceeded the speed limit during this trip.
B)The car must have exceeded the speed limit at some point during this trip.
C)There is not enough information to determine whether the car exceeded the speed limit during this trip.
D)The car's speed was 100 km/hr during the whole trip.

Question 40

At time,t = 0 s,car A is at rest at the origin of the coordinate system and car B is moving due East at a constant velocity of 20 m/s.When car B is 50 m west of car A,car A starts to move at a constant acceleration of 2 m/s² due East.How far from the origin has car A moved when car B overtakes car A?

A)20.0 m
B)8.58 m
C)14.3 m
D)2.0 m
E)4.36 m

Question 41

A firecracker is fired straight up with a speed of 100 m/s.Neglecting air resistance,the maximum height it will attain is

A)510 m.
B)325 m.
C)280 m.
D)129 m.

Question 42

A helicopter lifts off at a constant acceleration of 2.3 m/s² upward.When after liftoff is the speed of the above helicopter 10.0 m/s?

A)2.8 s
B)2.9 s
C)4.0 s
D)4.3 s

Question 43

Starting from rest,a car accelerates at a rate of +4 m/s² for 3 seconds.The car then travels at a constant speed for 5 seconds.What is the displacement of the car after moving for a total of 8 seconds?

A)32 m
B)36 m
C)72 m
D)78 m
E)128 m

Question 44

The position of a particle as a function of time along the x-axis is given by x = ((5 m)+ (12 m/s)t - (4 m/s²)t² ).What is the speed of the particle when its position is x = 14 m?

A)0 m/s
B)5 m/s
C)12 m/s
D)24 m/s
E)60 m/s

Question 45

The graph is of position versus time.Which statement best describes it?

A)The velocity is always positive.
B)The acceleration is constant.
C)The velocity is first negative and then positive.
D)The acceleration is zero or negative.
E)The velocity is never zero.

Question 46

An elevator is moving up with 8 m/s when a bolt came loose from the bottom.The bolt reaches the bottom of the shaft in 4 seconds.The velocity of the bolt at the bottom is

A)39 m/s.
B)21 m/s.
C)-31.2 m/s.
D)-47.2 m/s.

Question 47

A helicopter lifts off at a constant acceleration of 2.3 m/s² upward.What is the height of the helicopter 2.5 s after liftoff?

A)6.6 m
B)7.2 m
C)13 m
D)14 m

Question 48

An object with constant acceleration has velocity of 12 m/s when its position is x = 8 m.At another position x = 16 m,its velocity is 20 m/s.Its acceleration is

A)1 m/s².
B)5 m/s².
C)7 m/s².
D)16 m/s².

Question 49

A car starts from rest and travels east for 50 km,stops and travels west for 30 km to finish the trip.What is the distance traveled (start to finish)of the car during this trip?

A)80 km
B)80 km east
C)20 km east
D)20 km
E)the correct distance traveled is not listed

Question 50

A football player is standing on the 10 yard line.He runs forward to the 40 yard line and then runs backwards to the 30 yard line.What is the distance that he has traveled and what is his displacement?

A)distance = 20 yards,displacement = 20 yards forward
B)distance = 20 yards,displacement = 30 yards forward
C)distance = 30 yards,displacement = 30 yards forward
D)distance = 40 yards,displacement = 20 yards forward
E)distance = 40 yards,displacement = 40 yards forward

Question 51

A car can accelerate from zero to 164 m/s in 469 meters.How long (in seconds)does it take to do this?

A)5.7
B)2.3
C)1.2
D)13.2
E)112

Question 52

A runner of mass 61.3 kg starts from rest and accelerates with a constant acceleration of 1.07 m/s² until she reaches a velocity of 8.1 m/s.She then continues running with this constant velocity.How far has she run (in meters)after 49.1 seconds?

A)195.88
B)229.18
C)268.14
D)313.72
E)367.05

Question 53

A car is traveling with a speed of 24 m/s.What is the magnitude of the acceleration necessary to stop the car in a distance of 60 m?

A)0.4 m/s²
B)2.5 m/s²
C)4.8 m/s²
D)6.1 m/s²
E)9.6 m/s²

Question 54

A rocket,speeding along toward Alpha Centauri,has an acceleration a(t)= At².Assume that the rocket began at rest at the Earth (x = 0)at t = 0.Assuming it simply travels in a straight line from Earth to Alpha Centauri (and beyond),what fraction of the trip to Alpha Centauri has the rocket travelled when it has travelled half the time necessary to reach the star?

A)1/2
B)1/4
C)1/8
D)1/16
E)1/32

Question 55

A car starts from rest and travels east for 50 km,stops and travels west for 30 km to finish the trip.What is the displacement (start to finish)of the car during this trip?

A)80 km
B)80 km east
C)30 km east
D)30 km
E)the correct displacement is not listed

Question 56

A car starts from rest and travels east for 50 km,stops and travels west for 30 km to finish the trip.What is the displacement (start to finish)of the car during this trip?

A)80 km
B)80 km east
C)20 km east
D)20 km
E)the correct displacement is not listed

Question 57

A rocket,speeding along toward Alpha Centauri,has an acceleration a(t)= At².Assume that the rocket began at rest at the Earth (x = 0)at t = 0.Assuming it simply travels in a straight line from Earth to Alpha Centauri (and beyond),what is the ratio of the speed of the rocket when it has passed the star to the speed when it has travelled half the time necessary to reach Alpha Centauri?

A)2
B)4
C)8
D)16
E)32

Question 58

A rocket,speeding along toward Alpha Centauri,has an acceleration a(t)= At².Assume that the rocket began at rest at the Earth (x = 0)at t = 0.Assuming it simply travels in a straight line from Earth to Alpha Centauri (and beyond),what is the ratio of the speed of the rocket when it has covered half the distance to the star to its speed when it has travelled half the time necessary to reach Alpha Centauri?

A)
B)
C)
D)

Question 59

The distance between Sarnia and London Ontario,Canada is about 100 km.You cover first 50 km at 40 km/h.In order for you to travel with an average speed of 50 km/h for the entire trip,the speed to cover the second 50 km would be

A)50 km/h.
B)67 km/h.
C)78 km/h.
D)100 km/h.

Question 60

What is your average speed in m/s when you go from -2 m to 10 m in 3.2 s and then from 10 m to -12 m in 5.4 seconds?

A)-2.7
B)29.4
C)11.2
D)3.95
E)0.34

Question 61

A drag racer reaches 150 km/hr in a 2-km race.Assuming constant acceleration,what was the elapsed time for the km (in minutes)?

A)1.4 min
B)1.6 min
C)1.8 min
D)2.0 min
E)2.2 min

Question 62

A plane lands at 50.0 m/s,and its brakes are capable of slowing it down at 10.0 m/s².How far does it go (in m)between touching down and stopping?

A)9.81
B)50.
C)125.
D)500.
E)250.

Question 63

The graph shown is of position versus time.Which statement best describes it?

A)v reaches a maximum of about 200 m/s.
B)a is always negative.
C)a is both positive and negative.
D)v decreases with time.
E)The velocity is never zero.

Question 64

An object starts from the origin and goes along the x-axis to x = 10 m in 2 s,stops for 5.5 s,and then travels at v = -4 m/s for 2.5 s? What is the average speed and velocity in m/s?

A)speed = 2,velocity = 2
B)speed = 2,velocity = 0
C)speed = 2,velocity = -2
D)speed = 0,velocity = 0
E)speed = 4,velocity = 0

Question 65

What is your average speed in m/s when you start from the origin and go along the x-axis at v = 10 m/s for 2 s,stops for 5 s,and then travels at v = -4 m/s for 3 s?

A)-2.7
B)3.2
C)4.0
D)1.0
E)0.80

Question 66

A ball is thrown directly down from the top of a building with a speed of 12 m/s,and it lands on the ground with a velocity 3 times the initial velocity.How high is the building (in meters)?

A)12
B)59
C)234
D)4320
E)8760

Question 67

The graph shown is of velocity versus time.Which statement best describes the acceleration?

A)The acceleration is never zero.
B)The acceleration is maximum near t = 10 s.
C)The acceleration is minimum near t = 10.
D)The acceleration is minimum near t = 100 at about -0.15 m/s².
E)The average value of the acceleration is about 0.08 m/s².

Question 68

A fish takes 14 minutes to swim 1 mile up a river.At this point a dam breaks and causes a current of 36 miles per hour to push him 0.6 miles downstream in 1 minute.What is the fish's average velocity for this entire trip?

A)0.0004 mph
B)0.017 mph
C)1.6 mph
D)2.4 mph
E)35 mph

Question 69

The figure shows the position of a car (black circles)at one second intervals.What is the velocity at the time t = 4 s?

A)-12 m/s
B)-8 m/s
C)0
D)8 m/s
E)12 m/s

Question 70

A runner starts from rest and runs a distance of 100 m in 10.0 s.What is his average acceleration in m/s²?

A)9.81
B)1.40
C)2.00
D)98.6
E)3.50

Question 71

The figure shows the position of a car (black circles)at one second intervals.What is the acceleration at the time t = 4 s?

A)-2 m/s²
B)-1 m/s²
C)0
D)1 m/s²
E)2 m/s²

Question 72

If you drop an object from the top of a high building,how long does it take for the object to reach a speed of 100 km/h?

A)0.124 s
B)2.83 s
C)5.11 s
D)9.81 s
E)12.3 s

Question 73

A police officer spots a speeding car traveling at 20 m/s (approximately 44 mph)as it passes.The officer immediately starts to drive,accelerating from rest at a rate of 5 m/s².How far will the officer have to drive before catching up to the speeding car?

A)100 m
B)80 m
C)500 m
D)16 m
E)160 m

Question 74

In this graph of distance vs.time,which of the following is true (chose one)?

A)The speed is negative.
B)The velocity is negative.
C)The velocity is positive.
D)The acceleration is negative.
E)The acceleration is positive.

Question 75

A rocket accelerates uniformly from 1000 to 4000 m/s over a distance of 5 km.How long did it take in seconds?

A)0.15
B)2
C)15
D)156
E)983

Question 76

The graph shown is of velocity versus time.Approximately when is the acceleration zero?

A)Near t = 50 s.
B)Near t = 10 s.
C)Near t = 20 s.
D)The acceleration is never zero.
E)Near t= 100 s.

Question 77

A car starts with a speed of 50 m/s and goes a distance of 1000 m in 10.0 s.What is its average acceleration?

A)10 m/s²
B)1.40 m/s²
C)2.00 m/s²
D)98.6 m/s²
E)3.50 m/s²

Question 78

A stone is dropped from a height of 20.0 m.How long does it take for it to hit the ground?

A)1.00 s
B)2.02 s
C)1.43 s
D)0.50 s
E)2.37 s

Question 79

In this graph of distance vs.time,which of the following is true (chose one)?

A)The velocity is constant.
B)The acceleration is sometimes negative and sometimes positive.
C)The acceleration is always zero.
D)The acceleration is always positive.
E)The acceleration is always negative.

Question 80

A ball is thrown with velocity of 10m/s upwards.If the ball is caught 1 m above its initial position,what is the speed of the ball when it is caught?

A)5.3 m/s
B)6.8 m/s
C)9.0 m/s
D)10 m/s
E)22 m/s