Q: A projectile is launched with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for its range on level ground?

$$\frac{v_0$^2 \sin(2\theta)}{g}$$

Q: A $$2\ \mathrm{kg}$$ object moves with velocity $$3\ \mathrm{m/s}. $$What is its kinetic energy?

$$0.5 \times 2 \times 3^2$ = 9\ \mathrm{J}$$

Q: A box is pushed across a floor with a force of $$10\ \mathrm{N}$$ over a distance of $$5\ \mathrm{m} at an $$angle of $$60^\circ to $$the direction of motion. How much work is done by the force?

$$W = 10 \times 5 \times \cos 60^\circ = 25\ \mathrm{J}$$

Q: A $$5\ \mathrm{kg}$$ object is dropped from a height of $$10\ \mathrm{m}. $$What is the work done by gravity?

$$W = mgh = 5 \times 9.8 \times 10 = 490\ \mathrm{J}$$

Q: A $$1\ \mathrm{kg}$$ ball is thrown straight up with an initial velocity of $$10\ \mathrm{m/s}. $$What is its maximum height? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_i^2$}{2g} = \frac{10^2$}{2 \times 9.8} \approx 5.1\ \mathrm{m}$$

Question 1

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

Accepted Answer

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

Question 2

Which of the following equations correctly gives the displacement $$\Delta x$$ for an object under constant acceleration?

Accepted Answer

$$\Delta x = v_i t + \frac{1}{2} a t^2$

Question 3

A projectile is launched with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its range on level ground?

Accepted Answer

$$\frac{v_0$^2 \sin(2	heta)}{g}$$

Question 4

Car A has a head start and is $$D$$ meters ahead of Car B. Car A moves at constant speed $$v_A$$, and Car B starts from rest and moves at constant speed $$v_B \u003e v_A. $$How long after Car B starts will it catch up to Car A?

Accepted Answer

$$\frac{D}{v_B - v_A}$$

Question 5

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy can never be negative.

Question 6

A $$2\ \mathrm{kg}$$ object moves with velocity $$3\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$0.5 	imes 2 	imes 3^2$ = 9\ \mathrm{J}$$

Question 7

Which equation represents the work done by a constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta to $$the displacement?

Accepted Answer

$$W = F d \cos 	heta$$

Question 8

A box is pushed across a floor with a force of $$10\ \mathrm{N}$$ over a distance of $$5\ \mathrm{m} at an $$angle of $$60^\circ to $$the direction of motion. How much work is done by the force?

Accepted Answer

$$W = 10 	imes 5 	imes \cos 60^\circ = 25\ \mathrm{J}$$

Question 9

Which of the following is the correct expression for the net work done on an object, according to the work-energy theorem?

Accepted Answer

$$W_{net} = \Delta K = \frac{1}{2} m v_f^2$ - \frac{1}{2} m v_i^2$

Question 10

A $$5\ \mathrm{kg}$$ object is dropped from a height of $$10\ \mathrm{m}. $$What is the work done by gravity?

Accepted Answer

$$W = mgh = 5 	imes 9.8 	imes 10 = 490\ \mathrm{J}$$

Question 11

Which formula gives the average velocity $$v_{avg}$$ over a time interval $$\Delta t$$?

Accepted Answer

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

Question 12

A force $$F(x)$$ varies with position $$x. $$Which integral gives the total work done by this force from $$x_i to$$ $$x_f$$?

Accepted Answer

$$W = \int_{x_i}^{x_f} F(x) dx$$

Question 13

A $$1\ \mathrm{kg}$$ ball is thrown straight up with an initial velocity of $$10\ \mathrm{m/s}. $$What is its maximum height? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_i^2$}{2g} = \frac{10^2$}{2 	imes 9.8} \approx 5.1\ \mathrm{m}$$

Question 14

Which of the following best describes the meaning of acceleration?

Accepted Answer

The rate of change of velocity with respect to time.

Question 15

A block slides down a frictionless incline. Which equation correctly gives its acceleration?

Accepted Answer

$$a = g \sin 	heta$$

Question 16

A $$3\ \mathrm{kg}$$ object is acted on by a net force of $$12\ \mathrm{N}. $$What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{12}{3} = 4\ \mathrm{m/s^2$}$$

Question 17

Which of the following is the correct formula for the frictional force acting on an object?

Accepted Answer

$$F = \mu n$$

Question 18

A $$10\ \mathrm{kg}$$ box rests on a horizontal surface. What is the normal force acting on it?

Accepted Answer

$$N = m g = 10 	imes 9.8 = 98\ \mathrm{N}$$

Essential Kinematics, Dynamics, and Work-Energy Principles in Physics

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