Q: A ball is dropped from rest from a height of 45 m. Ignoring air resistance, how long does it take to reach the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

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

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which equation gives the maximum height reached?

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

Q: A 10 kg box is at rest on a horizontal surface. The coefficient of static friction is 0.4. What is the maximum force that can be applied horizontally before the box starts to move?

$$F_{max} = \mu_s N = 0.4 \times 10 \times 9.8 = 39.2\ \mathrm{N}$$

Q: A block slides down a frictionless incline of height 5 m. What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} \approx 9.9\ \mathrm{m/s}$$

Q: A 5 kg object is lifted vertically by 3 m. How much work is done against gravity?

$$W = mgh = 5 \times 9.8 \times 3 = 147\ \mathrm{J}$$

Question 1

A car travels 60 km north, then 80 km east. What is the magnitude of its displacement?

Accepted Answer

$$\sqrt{60^2$ + 80^2$} = 100\ \mathrm{km}$$

Question 2

Which of the following best describes the difference between velocity and speed?

Accepted Answer

Velocity is a vector quantity, while speed is a scalar quantity.

Question 3

A ball is dropped from rest from a height of 45 m. Ignoring air resistance, how long does it take to reach the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 4

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the maximum height reached?

Accepted Answer

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

Question 5

A cyclist moves in a circle of radius 20 m at a constant speed of 5 m/s. What is the magnitude of the centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{5^2$}{20} = 1.25\ \mathrm{m/s^2$}$$

Question 6

A 10 kg box is at rest on a horizontal surface. The coefficient of static friction is 0.4. What is the maximum force that can be applied horizontally before the box starts to move?

Accepted Answer

$$F_{max} = \mu_s N = 0.4 	imes 10 	imes 9.8 = 39.2\ \mathrm{N}$$

Question 7

A 2 kg object is acted upon by a net force of 10 N. What is its acceleration?

Accepted Answer

$$a = \frac{F_{net}}{m} = \frac{10}{2} = 5\ \mathrm{m/s^2$}$$

Question 8

A block slides down a frictionless incline of height 5 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9\ \mathrm{m/s}$$

Question 9

A 5 kg object is lifted vertically by 3 m. How much work is done against gravity?

Accepted Answer

$$W = mgh = 5 	imes 9.8 	imes 3 = 147\ \mathrm{J}$$

Question 10

A car accelerates from rest to 20 m/s in 5 seconds. What is its average acceleration?

Accepted Answer

$$a_{avg} = \frac{\Delta v}{\Delta t} = \frac{20}{5} = 4\ \mathrm{m/s^2$}$$

Question 11

A 0.2 kg ball moving at 10 m/s collides elastically with a stationary 0.3 kg ball. What is the velocity of the 0.2 kg ball after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{0.2 - 0.3}{0.2 + 0.3} 	imes 10 = -2\ \mathrm{m/s}$$

Question 12

A rocket expels gas at a constant rate. Which principle explains its propulsion?

Accepted Answer

Conservation of momentum

Question 13

A 2 kg mass is attached to a spring with spring constant $$k = 50\ \mathrm{N/m}$$ and compressed by 0.1 m. What is the elastic potential energy stored?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 50 	imes (0.1)^2$ = 0.25\ \mathrm{J}$$

Question 14

A 0.5 kg ball moving at 4 m/s collides inelastically with a 0.5 kg ball at rest. What is their final velocity?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{0.5 	imes 4 + 0.5 	imes 0}{1.0} = 2\ \mathrm{m/s}$$

Question 15

A spinning disk has an angular velocity of $$10\ \mathrm{rad/s}$$ and a radius of $$0.2\ \mathrm{m}. $$What is the linear velocity at the edge?

Accepted Answer

$$v = \omega r = 10 	imes 0.2 = 2\ \mathrm{m/s}$$

Question 16

A 3 kg object moves at 6 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 3 	imes 36 = 54\ \mathrm{J}$$

Question 17

A 2 kg object moving at 3 m/s collides elastically with a 1 kg object at rest. What is the velocity of the 1 kg object after the collision?

Accepted Answer

$$v_2$$' = \frac{2 $$m_1$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{2 	imes 2}{2 + 1} 	imes 3 = 4\ \mathrm{m/s}$$

Question 18

A 1 kg mass is whirled in a circle of radius 0.5 m at 4 m/s. What is the tension in the string?

Accepted Answer

$$T = m \frac{v^2$}{r} = 1 	imes \frac{16}{0.5} = 32\ \mathrm{N}$$

Physics I Syllabus and Topic Overview: Kinematics, Dynamics, and Energy

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