Q: A ball is dropped from rest from a height of 20 m. Ignoring air resistance, what is its speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 20} = 19.8\ \mathrm{m/s}$$

Q: A car of mass $$1200\ \mathrm{kg}$$ accelerates from rest to $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the average force exerted by the engine?

$$F = ma = \frac{m(v_f - v_i)}{t} = \frac{1200 \times 20}{10} = 2400\ \mathrm{N}$$

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

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 2 \times 9 = 9\ \mathrm{J}$$

Q: A $$0.2\ \mathrm{kg}$$ apple falls from a tree branch $$3\ \mathrm{m}$$ above the ground. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 3} = 7.67\ \mathrm{m/s}$$

Q: A $$3\ \mathrm{kg}$$ object moving at $$2\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object at rest. What is their final velocity after collision?

$$v_f = \frac{m_1v_1 + m_2v_2}{m_1$ + m_2$} = \frac{3 \times 2 + 2 \times 0}{3 + 2} = 1.2\ \mathrm{m/s}$$

Q: A $$10\ \mathrm{kg}$$ box is lifted vertically $$2\ \mathrm{m}. $$How much work is done against gravity? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$W = mgh = 10 \times 9.8 \times 2 = 196\ \mathrm{J}$$

Question 1

A ball is dropped from rest from a height of 20 m. Ignoring air resistance, what is its speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} = 19.8\ \mathrm{m/s}$$

Question 2

Which of the following best describes the difference between elastic and inelastic collisions?

Accepted Answer

Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum.

Question 3

A car of mass $$1200\ \mathrm{kg}$$ accelerates from rest to $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the average force exerted by the engine?

Accepted Answer

$$F = ma = \frac{m(v_f - v_i)}{t} = \frac{1200 	imes 20}{10} = 2400\ \mathrm{N}$$

Question 4

A $$0.5\ \mathrm{kg}$$ ball moving at $$4\ \mathrm{m/s}$$ collides head-on with a stationary $$0.5\ \mathrm{kg}$$ ball in an elastic collision. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_1$$' = 0\ \mathrm{m/s}$$

Question 5

Which of the following is the correct expression for gravitational potential energy near Earth's surface?

Accepted Answer

$$U = mgh$$

Question 6

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

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 2 	imes 9 = 9\ \mathrm{J}$$

Question 7

A $$5\ \mathrm{kg}$$ box is pushed across a floor with a constant velocity by a $$20\ \mathrm{N}$$ force. What is the frictional force acting on the box?

Accepted Answer

$$F_{friction} = 20\ \mathrm{N}$$

Question 8

A $$0.2\ \mathrm{kg}$$ apple falls from a tree branch $$3\ \mathrm{m}$$ above the ground. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 3} = 7.67\ \mathrm{m/s}$$

Question 9

Which of the following statements about Newton's Third Law is correct?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 10

A $$0.1\ \mathrm{kg}$$ ball is thrown vertically upward with a speed of $$10\ \mathrm{m/s}. $$What is its maximum height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{100}{19.6} = 5.1\ \mathrm{m}$$

Question 11

A $$3\ \mathrm{kg}$$ object moving at $$2\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object at rest. What is their final velocity after collision?

Accepted Answer

$$v_f = \frac{m_1v_1 + m_2v_2}{m_1$ + m_2$} = \frac{3 	imes 2 + 2 	imes 0}{3 + 2} = 1.2\ \mathrm{m/s}$$

Question 12

Which of the following is the correct SI unit for power?

Accepted Answer

$$\mathrm{Watt\ (W)}$$

Question 13

A $$10\ \mathrm{kg}$$ box is lifted vertically $$2\ \mathrm{m}. $$How much work is done against gravity? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = mgh = 10 	imes 9.8 	imes 2 = 196\ \mathrm{J}$$

Question 14

A $$0.5\ \mathrm{kg}$$ cart moving at $$2\ \mathrm{m/s}$$ collides elastically with a $$1.0\ \mathrm{kg}$$ cart at rest. What is the velocity of the $$0.5\ \mathrm{kg}$$ cart after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$}$$v_1$$ = \frac{0.5 - 1.0}{0.5 + 1.0} 	imes 2 = -0.67\ \mathrm{m/s}$$

Question 15

Which formula gives the impulse delivered to an object?

Accepted Answer

$$J = F \Delta t$$

Question 16

A $$2\ \mathrm{kg}$$ object falls freely from rest for $$3\ \mathrm{s}. $$What is its velocity after $$3\ \mathrm{s}$$? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = gt = 9.8 	imes 3 = 29.4\ \mathrm{m/s}$$

Question 17

A $$1.5\ \mathrm{kg}$$ object is moving at $$4\ \mathrm{m/s}$$ and comes to rest in $$2\ \mathrm{s}$$ due to friction. What is the magnitude of the frictional force?

Accepted Answer

$$F = ma = m \frac{\Delta v}{\Delta t} = 1.5 	imes \frac{4}{2} = 3.0\ \mathrm{N}$$

Question 18

Which of the following is a vector quantity?

Accepted Answer

Velocity

Question 19

A $$0.3\ \mathrm{kg}$$ ball is thrown horizontally at $$5\ \mathrm{m/s}$$ from a $$10\ \mathrm{m}$$ high cliff. How long does it take to hit the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{20}{9.8}} = 1.43\ \mathrm{s}$$

Fundamental Principles and Laws in Introductory Physics

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