Question 1

Two cars are traveling around identical circular racetracks.Car A travels at a constant speed of 20 m/s.Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s.When car B has the same (tangential)velocity as car A,it is always true that:
A)it is passing car A.
B)it has the same linear (tangential)acceleration as car A.
C)it has the same centripetal acceleration as car A.
D)it has the same total acceleration as car A.
E)it has traveled farther than car A since starting.

Accepted Answer

When both cars have the same tangential velocity, they are traveling at the same speed, but in different positions along the circular track. Since they are traveling at the same speed, they have the same tangential acceleration. However, their centripetal accelerations are determined by their positions on the track, which are different. Therefore, car B does not necessarily have the same centripetal acceleration as car A until it reaches the same position on the track. However, once it reaches that position, it will have the same centripetal acceleration as car A, since both are traveling at the same speed and radius. The other choices are incorrect because there is no information provided about passing or total distance traveled, and the tangential acceleration is already stated to be constant for car B.

Question 2

Given the equations below,which description best fits the physical situation? 
A)A projectile's displacement two seconds after being fired upward with a speed of 30.0 m/s.
B)A projectile's displacement two seconds after being fired upward with a speed of 40.0 m/s.
C)A projectile's displacement two seconds after being fired upward with a speed of 50.0 m/s.
D)A projectile's displacement two seconds after being fired upward with a speed of 60.0 m/s.
E)A projectile's displacement two seconds after being fired upward with a speed of 80.0 m/s.

Accepted Answer

The answer of Given the equations below,which description best fits...

Question 3

Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides in the direction of rotation of the merry-go-round?
A)5.03 s
B)8.37 s
C)12.6 s
D)25.1 s
E)50.2 s

Accepted Answer

The answer of Refer to Exhibit 4-1.At what time intervals...

Question 4

A block is supported on a compressed spring,which projects the block straight up in the air at velocity 
)The spring and ledge it sits on then retract.You can win a prize by hitting the block with a ball.When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block. )
A)At the instant when the block leaves the spring,directed at the block.
B)At the instant when the block leaves the spring,directed at the spring.
C)At the instant when the block is at the highest point,directed at the block.
D)At the instant when the block is at the highest point,directed at the spring.
E)When the block is back at the spring's original position,directed at that position.

Accepted Answer

When the block is at the highest point, it is momentarily at rest before falling back down due to gravity. This is the best time to throw the ball because it is stationary relative to the thrower. Additionally, throwing the ball at the block ensures that the ball hits the target and potentially wins the prize. Throwing the ball at the spring or the original position of the spring would not guarantee hitting the block, and throwing the ball when the block leaves the spring would require precise timing and accuracy. Therefore, choice C is the best option.

Question 5

The position of an object is given by Where t is in seconds.At t = 2.0 s,what is the magnitude of the particle's acceleration? A)0 m/s² B)2.0 m/s² C)17 m/s² D)36 m/s² E)72 m/s²

Accepted Answer

The answer of The position of an object is given...

Question 6

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:
A)is less than that observed inside the bus.
B)is the same as that observed inside the bus.
C)is greater than that observed inside the bus.
D)may be either greater or smaller than that observed inside the bus.
E)may be either greater,smaller,or equal to that observed inside the bus.

Accepted Answer

The answer of A student in the front of a...

Question 7

With the x axis horizontal and the y axis vertically upward,the change in the horizontal component of velocity,Δv_x,and the change in the vertical component of velocity,Δv_y,of a projectile are related to the time since leaving the barrel,Δt,as A)Δv_x = 0;Δv_y = 0. B)Δv_x = gΔt;Δv_y = 0. C)Δv_x = 0;Δv_y = gΔt. D)Δv_x = 0;Δv_y = −gΔt. E)Δv_x = gΔt;Δv_y = −gΔt.

Accepted Answer

In projectile motion, the horizontal component of velocity remains constant (no acceleration in the horizontal direction) because gravity only affects the vertical motion. Therefore, Δvx = 0. The change in the vertical component of velocity, Δvy, is due to gravity, which acts downward, making Δvy = -gΔt, where g is the acceleration due to gravity.

Question 8

In a location where the train tracks run parallel to a road,a high speed train traveling at 60 m/s passes a car traveling at 30 m/s.How long does it take for the train to be 180 m ahead of the car?
A)2.0 s
B)3.0 s
C)6.0 s
D)9.0 s
E)18.0 s

Accepted Answer

The relative velocity between the train and the car is 60 m/s - 30 m/s = 30 m/s. 
To cover a distance of 180 m at this relative velocity, the time required is:
time = distance/relative velocity = 180 m/30 m/s = 6.0 s. 
Therefore, the train will be 180 m ahead of the car in 6.0 s.

Question 9

Which of the following quantities is directly proportional to the time interval after a projectile has left the barrel that shot it out? The x axis is horizontal;the y axis is vertically upward. A) B)Δa_y C)Δy D) E)Δv_y

Accepted Answer

The vertical displacement of a projectile is given by the equation Δy = v₀t + 1/2gt², where v₀ is the initial vertical velocity, t is the time interval after the projectile has left the barrel, g is the acceleration due to gravity, and t² represents the square of the time interval. The change in vertical velocity is given by the equation Δv = gt, where g is the acceleration due to gravity and t is the time interval after the projectile has left the barrel. Therefore, Δv/Δt = g, which is a constant value. This means that the change in vertical velocity is directly proportional to the time interval after the projectile has left the barrel, and the answer is E, Δv/Δt, which is equivalent to (v - v₀)/t.

Question 10

A car travels around an oval racetrack at constant speed.The car is accelerating 
A)at all points except B and D.
B)at all points except A and C.
C)at all points except A,B,C,and D.
D)everywhere,including points A,B,C,and D.
E)nowhere,because it is traveling at constant speed.

Accepted Answer

The answer of A car travels around an oval racetrack...

Question 11

A projectile starts at the coordinate origin,where the displacement vector also originates.The initial velocity,v₀,makes an angle θ₀ with the horizontal where 0 < θ₀ < 90°.At the instant when the projectile is at the highest point of its trajectory,the displacement,velocity and acceleration vectors are , And )Which statement is true? A) is parallel to . B) is perpendicular to . C) is parallel to . D) is perpendicular to . E) is perpendicular to .

Accepted Answer

The displacement vector 11ea7ff9_2a6b_9857_a768_4d226ae1e42a_TB2295_11 is perpendicular to the velocity vector 11ea7ff9_2a6b_9858_a768_f9c04a9132d9_TB2295_11 at the highest point of the trajectory. This means that the acceleration vector 11ea7ff9_2a6c_0d8d_a768_bfd6ba145591_TB2295_11 is perpendicular to both the displacement and velocity vectors. Therefore, option D is true.

Question 12

Car A leaves point O at t = 0 and travels a quarter circle counterclockwise at 30.0 m/s to point P.Car B will leave point O and travel to point P at the same speed but in a straight line.The radius of the circle is 100 m.At what time should car B leave point O in order to arrive at point P at the same time as car A?
A)At t = 0.
B)At t = 0.52 s.
C)At t = 4.71 s.
D)At t = 4.98 s.
E)At t = 5.24 s.

Accepted Answer

The answer of Car A leaves point O at t...

Question 13

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by 
And 
)
The plane is most likely
A)just touching down.
B)in level flight in the air.
C)ascending.
D)descending.
E)taking off.

Accepted Answer

The answer of The site from which an airplane takes...

Question 14

Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides opposite to the direction of rotation of the merry-go-round?
A)5.03 s
B)8.37 s
C)12.6 s
D)25.1 s
E)50.2 s

Accepted Answer

The answer of Refer to Exhibit 4-1.At what time intervals...

Question 15

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by 
And 
)
The plane is most likely
A)just touching down.
B)in level flight in the air.
C)ascending.
D)descending.
E)taking off.

Accepted Answer

The velocity vector has a positive y component, indicating that the plane is moving upwards, or ascending.

Question 16

Two balls,projected at different times so they don't collide,have trajectories A and B,as shown below. Which statement is correct? A)v_0B must be greater than v_0A. B)Ball A is in the air for a longer time than ball B. C)Ball B is in the air for a longer time than ball A. D)Ball B has a greater acceleration than ball A. E)Ball A has a greater acceleration than ball B.

Accepted Answer

Ball B has a longer horizontal distance to cover due to its initial projection angle, therefore it stays in the air for a longer period of time than Ball A. The statements in options A, B, D, and E are not necessarily true based on the given information.

Question 17

Given the equations below,which description best fits the physical situation? 
A)A projectile's displacement two seconds after being fired downward with a speed of 30.0 m/s.
B)A projectile's displacement two seconds after being fired downward with a speed of 40.0 m/s.
C)A projectile's displacement two seconds after being fired downward with a speed of 50.0 m/s.
D)A projectile's displacement two seconds after being fired downward with a speed of 60.0 m/s.
E)A projectile's displacement two seconds after being fired downward with a speed of 80.0 m/s.

Accepted Answer

The answer of Given the equations below,which description best fits...

Question 18

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by 
And 
)
The plane is most likely
A)just touching down.
B)in level flight in the air.
C)ascending.
D)descending.
E)taking off.

Accepted Answer

The answer of The site from which an airplane takes...

Question 19

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by 
And 
)
The plane is most likely
A)just touching down.
B)in level flight in the air.
C)ascending.
D)descending.
E)taking off.

Accepted Answer

The answer of The site from which an airplane takes...

Question 20

The vector 
Indicates the instantaneous displacement of a projectile from the origin.At the instant when the projectile is at 
,its velocity and acceleration vectors are 
And 
)Which statement is correct?
A)  is always perpendicular to  .
B)  is always perpendicular to  .
C)  is always perpendicular to  .
D)  is always perpendicular to  .
E)  is always perpendicular to  .

Accepted Answer

The answer of The vector 
Indicates the instantaneous displacement of...

Quiz 4: Motion in Two Dimensions

Two cars are traveling around identical circular racetracks.Car A travels at a constant speed of 20 m/s.Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s.When car B has the same (tangential) velocity as car A,it is always true that:

Given the equations below,which description best fits the physical situation?

Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides in the direction of rotation of the merry-go-round?

The position of an object is given by Where t is in seconds.At t = 2.0 s,what is the magnitude of the particle's acceleration?

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:

With the x axis horizontal and the y axis vertically upward,the change in the horizontal component of velocity,Δv_x,and the change in the vertical component of velocity,Δv_y,of a projectile are related to the time since leaving the barrel,Δt,as

In a location where the train tracks run parallel to a road,a high speed train traveling at 60 m/s passes a car traveling at 30 m/s.How long does it take for the train to be 180 m ahead of the car?

Which of the following quantities is directly proportional to the time interval after a projectile has left the barrel that shot it out? The x axis is horizontal;the y axis is vertically upward.

A car travels around an oval racetrack at constant speed.The car is accelerating

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides opposite to the direction of rotation of the merry-go-round?

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

Two balls,projected at different times so they don't collide,have trajectories A and B,as shown below. Which statement is correct?

Given the equations below,which description best fits the physical situation?

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

The vector Indicates the instantaneous displacement of a projectile from the origin.At the instant when the projectile is at ,its velocity and acceleration vectors are And ) Which statement is correct?

Quiz 4: Motion in Two Dimensions

Two cars are traveling around identical circular racetracks.Car A travels at a constant speed of 20 m/s.Car B starts at rest and speeds up with constant tangential acceleration until its speed is 40 m/s.When car B has the same (tangential) velocity as car A,it is always true that:

Given the equations below,which description best fits the physical situation?

Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides in the direction of rotation of the merry-go-round?

The position of an object is given by Where t is in seconds.At t = 2.0 s,what is the magnitude of the particle's acceleration?

A student in the front of a school bus tosses a ball to another student in the back of the bus while the bus is moving forward at constant velocity.The speed of the ball as seen by a stationary observer in the street:

With the x axis horizontal and the y axis vertically upward,the change in the horizontal component of velocity,Δvx,and the change in the vertical component of velocity,Δvy,of a projectile are related to the time since leaving the barrel,Δt,as

In a location where the train tracks run parallel to a road,a high speed train traveling at 60 m/s passes a car traveling at 30 m/s.How long does it take for the train to be 180 m ahead of the car?

Which of the following quantities is directly proportional to the time interval after a projectile has left the barrel that shot it out? The x axis is horizontal;the y axis is vertically upward.

A car travels around an oval racetrack at constant speed.The car is accelerating

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

Refer to Exhibit 4-1.At what time intervals does Sheila encounter her brother,if she rides opposite to the direction of rotation of the merry-go-round?

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

Two balls,projected at different times so they don't collide,have trajectories A and B,as shown below. Which statement is correct?

Given the equations below,which description best fits the physical situation?

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

The site from which an airplane takes off is the origin.The x axis points east;the y axis points straight up.The position and velocity vectors of the plane at a later time are given by And ) The plane is most likely

The vector Indicates the instantaneous displacement of a projectile from the origin.At the instant when the projectile is at ,its velocity and acceleration vectors are And ) Which statement is correct?

With the x axis horizontal and the y axis vertically upward,the change in the horizontal component of velocity,Δv_x,and the change in the vertical component of velocity,Δv_y,of a projectile are related to the time since leaving the barrel,Δt,as