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

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Q: A student pushes a box across a rough floor with a force of 50 N for 4 m. The frictional force is 30 N. What is the net work done on the box?

$$W_{net} = (50 - 30) \times 4 = 80 J$$

Q: A 5 kg object is lifted vertically by 2 m. What is the work done against gravity?

$$W = mgh = 5 \times 9.8 \times 2 = 98 J$$

Q: A 0.5 kg ball is attached to a string and swung in a horizontal circle of radius 1.5 m at a speed of 4 m/s. What is the tension in the string?

$$T = \frac{mv^2$}{r} = \frac{0.5 \times 16}{1.5} \approx 5.33 N$$

Q: A 3 kg object moving at 5 m/s collides with a stationary 2 kg object and they stick together. What is their final velocity?

$$v_f = \frac{3 \times 5}{3 + 2} = 3 m/s$$

Q: A student lifts a 10 kg box from the ground to a shelf 1.5 m high in 3 seconds. What is the average power output?

$$P = \frac{mgh}{t} = \frac{10 \times 9.8 \times 1.5}{3} = 49 W$$

Q: A 1 kg object is dropped from a height of 10 m. What is its velocity just before hitting the ground?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} \approx 14 m/s$$

Question 1

A ball is thrown vertically upward with an initial velocity of $$v_0. $$Neglecting air resistance, which of the following equations correctly gives the maximum height $$h_{max}$$ reached by the ball?

Accepted Answer

$$h_{max} = \frac{v_0$^2}{2g}$$

Question 2

A car accelerates from rest at a constant rate $$a$$ for a time $$t. $$What is the final velocity $$v of $$the car?

Accepted Answer

$$v = a t$$

Question 3

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

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 4

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its speed $$v at $$the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 5

Which of the following best describes the work done by a constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta to $$the direction of displacement?

Accepted Answer

$$W = F d \cos 	heta$$

Question 6

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = 6 J$$

Question 7

A student pushes a box across a rough floor with a force of 50 N for 4 m. The frictional force is 30 N. What is the net work done on the box?

Accepted Answer

$$W_{net} = (50 - 30) 	imes 4 = 80 J$$

Question 8

A satellite orbits Earth in a circular path. Which force provides the necessary centripetal acceleration?

Accepted Answer

Gravitational force

Question 9

A 5 kg object is lifted vertically by 2 m. What is the work done against gravity?

Accepted Answer

$$W = mgh = 5 	imes 9.8 	imes 2 = 98 J$$

Question 10

A car of mass $$m$$ moves in a circle of radius $$r at $$constant speed $$v. $$What is the centripetal force acting on the car?

Accepted Answer

$$F_c = \frac{mv^2$}{r}$$

Question 11

A student drops a ball from a height of 20 m. Neglecting air resistance, how long does it take to reach the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02 s$$

Question 12

A 0.5 kg ball is attached to a string and swung in a horizontal circle of radius 1.5 m at a speed of 4 m/s. What is the tension in the string?

Accepted Answer

$$T = \frac{mv^2$}{r} = \frac{0.5 	imes 16}{1.5} \approx 5.33 N$$

Question 13

A 3 kg object moving at 5 m/s collides with a stationary 2 kg object and they stick together. What is their final velocity?

Accepted Answer

$$v_f = \frac{3 	imes 5}{3 + 2} = 3 m/s$$

Question 14

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$PE = \frac{1}{2} k x^2$

Question 15

A student lifts a 10 kg box from the ground to a shelf 1.5 m high in 3 seconds. What is the average power output?

Accepted Answer

$$P = \frac{mgh}{t} = \frac{10 	imes 9.8 	imes 1.5}{3} = 49 W$$

Question 16

A cyclist increases her speed from 5 m/s to 15 m/s. By what factor does her kinetic energy increase?

Accepted Answer

The kinetic energy increases by a factor of 9, since $$KE \propto v^2$ and $$\left(\frac{15}{5}\$$right)^2 = 9$

Question 17

A 1 kg object is dropped from a height of 10 m. What is its velocity just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} \approx 14 m/s$$

Question 18

A student pushes a 4 kg box with a force of 20 N across a horizontal surface for 5 m. The frictional force is 8 N. What is the net work done?

Accepted Answer

$$W_{net} = (20 - 8) 	imes 5 = 60 J$$

Question 19

A 0.2 kg ball is thrown horizontally from a 45 m high cliff. How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{90}{9.8}} \approx 3.03 s$$

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