Question 1

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1$$, where $$x is in $$meters and $$t is in $$seconds. What is the instantaneous velocity of the car at $$t = 3 s$$?

Accepted Answer

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

Question 2

A runner completes a 100 m dash in 10 s. What is the runner's average velocity if she starts and finishes at the same point?

Accepted Answer

$$v_{\mathrm{avg}} = 0\ \mathrm{m/s}$$

Question 3

Which of the following statements about instantaneous velocity is correct?

Accepted Answer

It is the derivative of position with respect to time: $$v_x = \frac{dx}{dt}$$

Question 4

A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$What is its velocity at the highest point?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 5

A car accelerates from rest at a constant rate of $$2\ \mathrm{m/s^2$}$$ for $$5$$ seconds. What is its final velocity?

Accepted Answer

$$v_x = 10\ \mathrm{m/s}$$

Question 6

A stone is dropped from rest from a cliff. How far does it fall in the first 3 seconds? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$44.1\ \mathrm{m}$$

Question 7

Which equation correctly relates final velocity, initial velocity, acceleration, and displacement for constant acceleration?

Accepted Answer

$$v_x^2$ = v_{0x}^2 + 2a_x(x - x_0$)$$

Question 8

A swimmer swims 50 m in 40 s. What is her average speed?

Accepted Answer

$$1.25\ \mathrm{m/s}$$

Question 9

A car’s velocity changes from $$20\ \mathrm{m/s} to$$ $$10\ \mathrm{m/s} in$$ $$5$$ seconds. What is its average acceleration?

Accepted Answer

$$a_{\mathrm{avg}} = -2\ \mathrm{m/s^2$}$$

Question 10

Which of the following best describes the motion of a freely falling object (ignoring air resistance)?

Accepted Answer

It accelerates downward at a constant rate of $$9.8\ \mathrm{m/s^2$}$$

Question 11

A car moves with a constant acceleration. Which of the following position-time graphs best represents its motion?

Accepted Answer

A parabola

Question 12

A ball is thrown downward from a tall building with an initial velocity of $$5\ \mathrm{m/s}. $$What is its velocity after $$2$$ seconds? ($$g = 9.8\ \mathrm{m/s^2$}$$, downward is positive)

Accepted Answer

$$v = 24.6\ \mathrm{m/s}$$

Question 13

Which of the following is NOT a correct equation for motion with constant acceleration?

Accepted Answer

$$x = x_0$ + v$$_{0x}$$t + a_xt$$

Question 14

A car starts from rest and accelerates uniformly at $$3\ \mathrm{m/s^2$}. $$How far does it travel in $$4$$ seconds?

Accepted Answer

$$24\ \mathrm{m}$$

Question 15

A particle moves along the x-axis with velocity given by $$v_x = 5t^2$, where t$ is in seconds. What is the acceleration at t = 2$ s?

Accepted Answer

$$a_x = 20\ \mathrm{m/s^2$}$$

Question 16

A coin is dropped from rest from the Leaning Tower of Pisa. What is its velocity after $$2$$ seconds? ($$g = 9.8\ \mathrm{m/s^2$}$$, downward is positive)

Accepted Answer

$$v = 19.6\ \mathrm{m/s}$$

Question 17

Which of the following statements about average speed and average velocity is correct?

Accepted Answer

Average speed is always greater than or equal to the magnitude of average velocity.

Question 18

A car travels east at $$20\ \mathrm{m/s}$$ for $$5$$ seconds, then west at $$10\ \mathrm{m/s}$$ for $$5$$ seconds. What is the car's average velocity for the entire trip?

Accepted Answer

$$v_{\mathrm{avg}} = 5\ \mathrm{m/s}$$\ east

Question 19

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$How long does it take to reach its maximum height? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.04\ \mathrm{s}$$

Motion Along a Straight Line: Kinematics in One Dimension

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