Question 1

A car starts from rest and accelerates uniformly at $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

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

Question 2

Which of the following is a correct kinematic equation for constant acceleration?

Accepted Answer

$$x_f = x_i + v_i t + \frac{1}{2} a t^2$

Question 3

A ball is thrown straight up with an initial velocity of $$15\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height it reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$11.5\ \mathrm{m}$$

Question 4

An elevator moves downward and slows down at a steady rate of $$2\ \mathrm{m/s^2$}. It $$starts at $$10\ \mathrm{m/s}$$ downward and comes to a stop. How far does the elevator travel during this time?

Accepted Answer

$$25\ \mathrm{m}$$

Question 5

Which of the following statements about solving kinematics problems is correct?

Accepted Answer

You must choose a coordinate system and assign signs to vector components based on direction.

Question 6

A small ball rolls horizontally off a tabletop $$1.20\ \mathrm{m}$$ high and lands $$1.47\ \mathrm{m}$$ away from the table. What was its initial speed as it left the table? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.0\ \mathrm{m/s}$$

Question 7

Which of the following is NOT a valid step in solving a kinematics problem?

Accepted Answer

Assume all unknowns are zero.

Question 8

Bob starts from rest and accelerates at $$2\ \mathrm{m/s^2$} to $$catch up with Alice, who is $$10\ \mathrm{m}$$ ahead and moving at $$2\ \mathrm{m/s}$$ with zero acceleration. How long does it take Bob to catch up?

Accepted Answer

$$5.0\ \mathrm{s}$$

Question 9

Which equation gives the instantaneous velocity as a function of time for a position function $$x(t) = 3t^2$ + 2t + 6$$?

Accepted Answer

$$v(t) = 6t + 2$$

Question 10

Which of the following best describes the relationship between acceleration and the velocity vs. time graph?

Accepted Answer

Acceleration is the slope of the velocity vs. time graph.

Question 11

A projectile is launched horizontally from a $$20\ \mathrm{m}$$ high cliff. How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.02\ \mathrm{s}$$

Question 12

Which of the following is true about the number of independent kinematic equations for each dimension?

Accepted Answer

There are only two independent equations of motion for each dimension.

Question 13

If you have more unknowns than independent equations in a kinematics problem, what can you conclude?

Accepted Answer

The problem cannot be solved uniquely.

Question 14

A runner accelerates from $$4\ \mathrm{m/s} to$$ $$8\ \mathrm{m/s} in$$ $$2\ \mathrm{s}. $$What is the average acceleration?

Accepted Answer

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

Question 15

Which of the following is the correct expression for instantaneous acceleration?

Accepted Answer

$$a = \frac{dv}{dt}$$

Question 16

A car travels with a constant velocity of $$20\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$What is the displacement?

Accepted Answer

$$200\ \mathrm{m}$$

Question 17

Which of the following is a correct method to check your answer in a kinematics problem?

Accepted Answer

Check that the units are consistent using dimensional analysis.

Question 18

A position function is given by $$x(t) = 4t^3$ + 2t^2$ + 5. $$What is the acceleration as a function of time?

Accepted Answer

$$a(t) = 24t$$

Question 19

Which of the following is the correct formula for average velocity over a time interval $$\Delta t$$?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Kinematics and Solving Motion Problems: Study Notes

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