Question 1

A car starts from rest and accelerates uniformly at $$2.5\ \mathrm{m/s^2$}$$ for $$8.0\ \mathrm{s}. $$What is the car's velocity at the end of this time?

Accepted Answer

$$20\ \mathrm{m/s}$$

Question 2

A runner accelerates from rest to a top speed of $$11.2\ \mathrm{m/s} in$$ $$2.14\ \mathrm{s}. $$What is the runner's average acceleration during this phase?

Accepted Answer

$$5.23\ \mathrm{m/s^2$}$$

Question 3

A rocket is launched straight up with a constant acceleration of $$18\ \mathrm{m/s^2$}$$ for $$150\ \mathrm{s}. $$What is its final velocity at the end of this period?

Accepted Answer

$$2700\ \mathrm{m/s}$$

Question 4

A stone is dropped from a cliff and falls freely under gravity. If the height of the cliff is $$100\ \mathrm{m}$$, how long does it take to reach the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$4.5\ \mathrm{s}$$

Question 5

A volcano ejects a rock straight up at $$30\ \mathrm{m/s}. $$Ignoring air resistance, what is the velocity of the rock when it falls back into the crater?

Accepted Answer

$$-30\ \mathrm{m/s}$$

Question 6

Which of the following equations correctly relates displacement $$\Delta x$$, initial velocity $$v_{xi}$$, acceleration $$a_x$$, and time $$\Delta t$$ for constant acceleration?

Accepted Answer

$$\Delta x = v_{xi}\Delta t + \frac{1}{2}a_x\Delta t^2$

Question 7

A particle's position is given by $$x(t) = 2t^3$ - 8t^2$ + 6t + 2. $$What is its acceleration at $$t = 1\ \mathrm{s}$$?

Accepted Answer

$$-4\ \mathrm{m/s^2$}$$

Question 8

A projectile is launched at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$What is the correct expression for its initial vertical velocity component?

Accepted Answer

$$v_0$$ \sin 	heta$$

Question 9

A car is moving to the right and slowing down. Which of the following statements is true about its velocity and acceleration?

Accepted Answer

Velocity is positive, acceleration is negative.

Question 10

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? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.04\ \mathrm{s}$$

Question 11

Which of the following best describes the velocity-time graph for an object moving with constant negative acceleration?

Accepted Answer

A straight line with negative slope

Question 12

A car travels $$100\ \mathrm{m} in$$ $$10\ \mathrm{s} at $$constant velocity. What is its acceleration?

Accepted Answer

$$0\ \mathrm{m/s^2$}$$

Question 13

A feather and an apple are dropped from the same height in a vacuum. Which statement is correct?

Accepted Answer

They hit the ground at the same time.

Question 14

Which kinematic equation would you use to find the final velocity of an object given its initial velocity, acceleration, and displacement?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2a\Delta x$$

Question 15

A train moves with constant acceleration. Its velocity increases from $$10\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s}$$ over a distance of $$200\ \mathrm{m}. $$What is its acceleration?

Accepted Answer

$$2.0\ \mathrm{m/s^2$}$$

Question 16

A projectile is launched horizontally from a cliff. Which statement is true about its motion?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity increases due to gravity.

Question 17

A car moves with a velocity given by $$v(t) = 6t^2$ - 16t + 6. $$What is the car's acceleration at $$t = 2\ \mathrm{s}$$?

Accepted Answer

$$8\ \mathrm{m/s^2$}$$

Question 18

A ball is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a height of $$20\ \mathrm{m}. $$How fast is it moving just before it hits the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$21.2\ \mathrm{m/s}$$

Kinematics: Motion with Constant Acceleration and Graphical Analysis

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