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

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

Q: A person stands on a scale in an elevator that is accelerating upward at $$2 \ \mathrm{m/s^2$}. If $$the person's mass is $$70 \ \mathrm{kg}$$, what does the scale read?

$$F = m(g + a) = 70 \times (9.8 + 2) = 826 \ \mathrm{N}$$

Q: A force of $$10 \ \mathrm{N} is $$applied to push a box $$5 \ \mathrm{m}$$ along a horizontal surface. If the force is parallel to the displacement, what is the work done?

$$W = Fd = 10 \times 5 = 50 \ \mathrm{J}$$

Q: A projectile is launched at an angle of $$45^\circ$$ with an initial speed of $$20 \ \mathrm{m/s}. $$What is the maximum height reached?

$$h_{max} = \frac{v_0$^2 \sin^2$ \theta}{2g} = \frac{20^2$ \times (\frac{1}{2})}{2 \times 9.8} = \frac{400 \times 0.5}{19.6} \approx 10.2 \ \mathrm{m}$$

Q: A $$2 \ \mathrm{kg}$$ object is moving at $$5 \ \mathrm{m/s}$$ east. What is its momentum?

$$p = mv = 2 \times 5 = 10 \ \mathrm{kg \cdot m/s}$$ \ \text{east}

Q: A $$5 \ \mathrm{kg}$$ block is pulled up a $$30^\circ$$ incline with a force of $$40 \ \mathrm{N}$$ parallel to the incline. If the block moves $$3 \ \mathrm{m}$$, what is the work done by the force?

$$W = Fd = 40 \times 3 = 120 \ \mathrm{J}$$

Q: A $$1 \ \mathrm{kg}$$ object is dropped from a height of $$10 \ \mathrm{m}. $$What is its speed just before hitting the ground?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = \sqrt{196} = 14 \ \mathrm{m/s}$$

Question 1

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

Accepted Answer

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

Question 2

Given the velocity function $$v(t) = 3t^2$ - 2t + 4$$, what is the displacement of the object from $$t = 0 to$$ $$t = 2$$ seconds?

Accepted Answer

$$\$$int_0$$^2 (3t^2$ - 2t + 4) \, dt = [t^3$ - t^2$ + 4t]_0^2$ = (8 - 4 + 8) - 0 = 12 \ \mathrm{m}$$

Question 3

A ball is thrown vertically upward with an initial velocity of $$20 \ \mathrm{m/s}. $$Neglecting air resistance, how long does it take to reach its maximum height?

Accepted Answer

$$t = \frac{v_0$}{g} = \frac{20}{9.8} \approx 2.04 \ \mathrm{s}$$

Question 4

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

Accepted Answer

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

Question 5

A person stands on a scale in an elevator that is accelerating upward at $$2 \ \mathrm{m/s^2$}. If $$the person's mass is $$70 \ \mathrm{kg}$$, what does the scale read?

Accepted Answer

$$F = m(g + a) = 70 	imes (9.8 + 2) = 826 \ \mathrm{N}$$

Question 6

A force of $$10 \ \mathrm{N} is $$applied to push a box $$5 \ \mathrm{m}$$ along a horizontal surface. If the force is parallel to the displacement, what is the work done?

Accepted Answer

$$W = Fd = 10 	imes 5 = 50 \ \mathrm{J}$$

Question 7

A car moving at $$30 \ \mathrm{m/s}$$ comes to a stop in $$5 \ \mathrm{s}$$ due to a constant braking force. What is the magnitude of the acceleration?

Accepted Answer

$$a = \frac{v_f - v_i}{t} = \frac{0 - 30}{5} = -6 \ \mathrm{m/s^2$}$$

Question 8

A projectile is launched at an angle of $$45^\circ$$ with an initial speed of $$20 \ \mathrm{m/s}. $$What is the maximum height reached?

Accepted Answer

$$h_{max} = \frac{v_0$^2 \sin^2$ 	heta}{2g} = \frac{20^2$ 	imes (\frac{1}{2})}{2 	imes 9.8} = \frac{400 	imes 0.5}{19.6} \approx 10.2 \ \mathrm{m}$$

Question 9

A $$2 \ \mathrm{kg}$$ object is moving at $$5 \ \mathrm{m/s}$$ east. What is its momentum?

Accepted Answer

$$p = mv = 2 	imes 5 = 10 \ \mathrm{kg \cdot m/s}$$ \ 	ext{east}

Question 10

A $$5 \ \mathrm{kg}$$ block is pulled up a $$30^\circ$$ incline with a force of $$40 \ \mathrm{N}$$ parallel to the incline. If the block moves $$3 \ \mathrm{m}$$, what is the work done by the force?

Accepted Answer

$$W = Fd = 40 	imes 3 = 120 \ \mathrm{J}$$

Question 11

A $$1 \ \mathrm{kg}$$ object is dropped from a height of $$10 \ \mathrm{m}. $$What is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = \sqrt{196} = 14 \ \mathrm{m/s}$$

Question 12

A $$3 \ \mathrm{kg}$$ object moving at $$4 \ \mathrm{m/s}$$ collides with a stationary $$2 \ \mathrm{kg}$$ object. If they stick together, what is their final velocity?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{3 	imes 4 + 2 	imes 0}{3 + 2} = \frac{12}{5} = 2.4 \ \mathrm{m/s}$$

Question 13

A $$10 \ \mathrm{kg}$$ box is at rest on a horizontal surface. The coefficient of static friction is $$0.4. $$What is the minimum force required to start moving the box?

Accepted Answer

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

Question 14

A $$2 \ \mathrm{kg}$$ object is moving in a circle of radius $$0.5 \ \mathrm{m} at a $$speed of $$4 \ \mathrm{m/s}. $$What is the centripetal force acting on it?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{2 	imes 16}{0.5} = \frac{32}{0.5} = 64 \ \mathrm{N}$$

Question 15

A $$5 \ \mathrm{kg}$$ object is moving at $$10 \ \mathrm{m/s}$$ and comes to rest in $$4 \ \mathrm{s}$$ due to a constant force. What is the magnitude of the force?

Accepted Answer

$$F = ma = m \frac{v_f - v_i}{t} = 5 	imes \frac{0 - 10}{4} = -12.5 \ \mathrm{N}$$

Question 16

A $$0.2 \ \mathrm{kg}$$ ball is thrown horizontally at $$15 \ \mathrm{m/s}$$ from a $$20 \ \mathrm{m}$$ high cliff. How far from the base of the cliff does it land?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02 \ \mathrm{s}$$; \ d = vt = 15 	imes 2.02 \approx 30.3 \ \mathrm{m}$

Question 17

A $$6 \ \mathrm{kg}$$ object is moving at $$8 \ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 6 	imes 64 = 3 	imes 64 = 192 \ \mathrm{J}$$

Question 18

A $$4 \ \mathrm{kg}$$ object is moving at $$3 \ \mathrm{m/s}$$ and collides elastically with a $$2 \ \mathrm{kg}$$ object at rest. What is the velocity of the $$4 \ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{4 - 2}{4 + 2} 	imes 3 = \frac{2}{6} 	imes 3 = 1 \ \mathrm{m/s}$$

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