Q: A car accelerates uniformly from rest and covers a distance of 200 m in 10 seconds. What is the car's acceleration?

$$a = \frac{2 \times 200}{10^2$} = 4 \ \mathrm{m/s^2$}$$

Q: A ball is thrown horizontally from the top of a 45 m high cliff. How long does it take to reach the ground? (Ignore air resistance, $$g = 9.8 \ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2 \times 45}{9.8}} \approx 3.03 \ \mathrm{s}$$

Q: A cyclist moves at a constant speed of 12 m/s for 30 seconds. What distance does the cyclist cover?

$$d = v t = 12 \times 30 = 360 \ \mathrm{m}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which equation gives the horizontal range (assuming level ground and neglecting air resistance)?

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

Q: A 5 kg box is pulled across a horizontal surface with a force of 20 N. If the coefficient of friction is $$\mu = 0.2$$, what is the acceleration of the box?

$$a = \frac{F - f_k}{m} = \frac{20 - (0.2 \times 5 \times 9.8)}{5} \approx 1.44 \ \mathrm{m/s^2$}$$

Q: A skydiver of mass 80 kg experiences a drag force of 600 N while falling. What is the net force acting on the skydiver?

$$F_{net} = mg - F_{drag} = 80 \times 9.8 - 600 = 184 \ \mathrm{N}$$

Q: A 2 kg object is attached to a spring and pulled so that the spring stretches 0.5 m. If the spring constant is $$k = 40 \ \mathrm{N/m}$$, what is the force exerted by the spring?

$$F = -k x = -40 \times 0.5 = -20 \ \mathrm{N}$$

Q: A person pushes a 10 kg box up a frictionless ramp inclined at $$30^\circ to $$the horizontal. What is the minimum force required to move the box up the ramp at constant speed?

$$F = mg \sin \theta = 10 \times 9.8 \times \sin 30^\circ = 49 \ \mathrm{N}$$

Q: A train accelerates from rest at $$2 \ \mathrm{m/s^2$}$$ for 20 seconds. What is its final velocity?

$$v_f = v_i + a t = 0 + 2 \times 20 = 40 \ \mathrm{m/s}$$

Q: A ball is dropped from a height of 80 m. How long does it take to reach the ground? ($$g = 9.8 \ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2 \times 80}{9.8}} \approx 4.04 \ \mathrm{s}$$

Question 1

A car accelerates uniformly from rest and covers a distance of 200 m in 10 seconds. What is the car's acceleration?

Accepted Answer

$$a = \frac{2 	imes 200}{10^2$} = 4 \ \mathrm{m/s^2$}$$

Question 2

A ball is thrown horizontally from the top of a 45 m high cliff. How long does it take to reach the ground? (Ignore air resistance, $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03 \ \mathrm{s}$$

Question 3

A cyclist moves at a constant speed of 12 m/s for 30 seconds. What distance does the cyclist cover?

Accepted Answer

$$d = v t = 12 	imes 30 = 360 \ \mathrm{m}$$

Question 4

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the horizontal range (assuming level ground and neglecting air resistance)?

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

A car rounds a curve of radius $$r at $$constant speed $$v. $$What is the required centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 7

A 5 kg box is pulled across a horizontal surface with a force of 20 N. If the coefficient of friction is $$\mu = 0.2$$, what is the acceleration of the box?

Accepted Answer

$$a = \frac{F - f_k}{m} = \frac{20 - (0.2 	imes 5 	imes 9.8)}{5} \approx 1.44 \ \mathrm{m/s^2$}$$

Question 8

A skydiver of mass 80 kg experiences a drag force of 600 N while falling. What is the net force acting on the skydiver?

Accepted Answer

$$F_{net} = mg - F_{drag} = 80 	imes 9.8 - 600 = 184 \ \mathrm{N}$$

Question 9

A 2 kg object is attached to a spring and pulled so that the spring stretches 0.5 m. If the spring constant is $$k = 40 \ \mathrm{N/m}$$, what is the force exerted by the spring?

Accepted Answer

$$F = -k x = -40 	imes 0.5 = -20 \ \mathrm{N}$$

Question 10

A person pushes a 10 kg box up a frictionless ramp inclined at $$30^\circ to $$the horizontal. What is the minimum force required to move the box up the ramp at constant speed?

Accepted Answer

$$F = mg \sin 	heta = 10 	imes 9.8 	imes \sin 30^\circ = 49 \ \mathrm{N}$$

Question 11

A train accelerates from rest at $$2 \ \mathrm{m/s^2$}$$ for 20 seconds. What is its final velocity?

Accepted Answer

$$v_f = v_i + a t = 0 + 2 	imes 20 = 40 \ \mathrm{m/s}$$

Question 12

A ball is dropped from a height of 80 m. How long does it take to reach the ground? ($$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2 	imes 80}{9.8}} \approx 4.04 \ \mathrm{s}$$

Question 13

A 3 kg object is acted upon by two forces: 10 N to the right and 4 N to the left. What is the acceleration of the object?

Accepted Answer

$$a = \frac{10 - 4}{3} = 2 \ \mathrm{m/s^2$}$$

Question 14

A car travels 100 m north, then 100 m east. What is the magnitude of its displacement?

Accepted Answer

$$d = \sqrt{100^2$ + 100^2$} = \sqrt{20000} \approx 141.4 \ \mathrm{m}$$

Question 15

A 50 kg crate is at rest on a horizontal floor. The coefficient of static friction is $$\mu_s = 0.4. $$What is the maximum force that can be applied before the crate starts to move?

Accepted Answer

$$F_{max} = \mu_s m g = 0.4 	imes 50 	imes 9.8 = 196 \ \mathrm{N}$$

Question 16

A runner accelerates from 5 m/s to 9 m/s in 4 seconds. What is the runner's acceleration?

Accepted Answer

$$a = \frac{9 - 5}{4} = 1 \ \mathrm{m/s^2$}$$

Question 17

A 2 kg object moves in a circle of radius 3 m at a speed of 6 m/s. What is the net force acting on the object?

Accepted Answer

$$F = m a_c = 2 	imes \frac{6^2$}{3} = 24 \ \mathrm{N}$$

Question 18

A 4 kg object is dropped from rest and falls for 5 seconds. What is its velocity just before hitting the ground? ($$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$v = v_0$ + g t = 0 + 9.8 	imes 5 = 49 \ \mathrm{m/s}$$

Question 19

A 10 kg box is pulled with a force of 40 N at an angle of $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k = 0.3. $$What is the horizontal acceleration of the box?

Accepted Answer

$$a = \frac{40 \cos 30^\circ - \mu_k m g}{m} = \frac{34.64 - 29.4}{10} = 0.524 \ \mathrm{m/s^2$}$$

Physics I: Kinematics and Newton's Laws - Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드