Question 1

A Japanese bullet train accelerates uniformly from rest and reaches a speed of $$300\ \mathrm{km/h} in$$ $$5$$ minutes. What is the average acceleration of the train in $$\mathrm{m/s^2$}$$?

Accepted Answer

$$0.017\ \mathrm{m/s^2$}$$

Question 2

Which of the following statements about the position-versus-time graph for uniform motion is correct?

Accepted Answer

The graph is a straight line, and its slope represents the object's velocity.

Question 3

Given the position function $$x(t) = 4t^2$ + 2t + 1$$, what is the instantaneous velocity at $$t = 3\ \mathrm{s}$$?

Accepted Answer

$$v = 26\ \mathrm{m/s}$$

Question 4

A car moves with a velocity described by $$v(t) = 4t\ \mathrm{m/s}. $$How far does the car travel in the first $$3$$ seconds?

Accepted Answer

$$18\ \mathrm{m}$$

Question 5

Bob leaves Chicago at $$9:00 AM $$driving east at $$60\ \mathrm{mph}$$, while Susan leaves Pittsburgh (400 miles east of Chicago) at the same time, driving west at $$40\ \mathrm{mph}. At $$what distance from Chicago do they meet?

Accepted Answer

$$200\ \mathrm{miles}$$

Question 6

If the velocity-versus-time graph of a particle is a straight line with a negative slope, what does this indicate about the particle's motion?

Accepted Answer

The particle is accelerating in the negative direction.

Question 7

Given the velocity function $$v(t) = 10 - 5t$$ for a particle starting at $$x_0 = 0$, at what time does the particle come to rest?

Accepted Answer

$$t = 3\ \mathrm{s}$$

Question 8

A position-versus-time graph has a slope of $$5\ \mathrm{m/s}$$ from $$t = 0 to$$ $$t = 2\ \mathrm{s}$$, then a slope of $$-2\ \mathrm{m/s}$$ from $$t = 2\ \mathrm{s} to$$ $$t = 4\ \mathrm{s}. $$What is the total displacement from $$t = 0 to$$ $$t = 4\ \mathrm{s}$$?

Accepted Answer

$$6\ \mathrm{m}$$

Question 9

Which of the following best describes the relationship between the area under a velocity-versus-time graph and the motion of an object?

Accepted Answer

The area under the curve gives the object's displacement.

Question 10

A particle moves according to $$x(t) = 2t^2$. What is the velocity at t = 4$$\ \mathrm{s}$$?

Accepted Answer

$$v = 16\ \mathrm{m/s}$$

Question 11

If a velocity-versus-time graph is a horizontal line at $$v = 0$$, what does the corresponding position-versus-time graph look like?

Accepted Answer

A horizontal line

Question 12

A drag racer’s velocity is given by $$v_x = 4t\ \mathrm{m/s}. $$What is the displacement after $$3\ \mathrm{s}$$?

Accepted Answer

$$18\ \mathrm{m}$$

Question 13

A particle starts at $$x_0 = 30$$\ \mathrm{m}$$ with a velocity graph given by v_x = 10 - 5t$. At what time does the particle reach the origin?

Accepted Answer

$$t = 4\ \mathrm{s}$$

Question 14

Which of the following is true about the slope of a position-versus-time graph?

Accepted Answer

It represents the object's velocity.

Question 15

If the velocity of a particle is zero at $$t = 2\ \mathrm{s}$$, what can be said about the position graph at that instant?

Accepted Answer

The position graph has a maximum or minimum (turning point).

Kinematics in One Dimension: Position, Velocity, and Calculus in Motion

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