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

$$t = \sqrt{\dfrac{2 \times 45}{9.8}}$$

Q: A runner accelerates uniformly from $$3\ \mathrm{m/s} to$$ $$9\ \mathrm{m/s}$$ over a distance of $$36\ \mathrm{m}. $$What is the acceleration?

$$a = \dfrac{(9^2$ - 3^2$)}{2 \times 36}$$

Q: A package is dropped from a helicopter hovering $$80\ \mathrm{m}$$ above the ground. How fast is it moving just before it hits the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$v = \sqrt{2 \times 9.8 \times 80}$$

Q: A skier starts from rest and accelerates down a frictionless slope at $$4\ \mathrm{m/s^2$}. $$How far does the skier travel in $$3$$ seconds?

$$x = \dfrac{1}{2} \times 4 \times 3^2$

Q: A ball is thrown upward with a velocity of $$15\ \mathrm{m/s}. $$How long does it take to return to the thrower's hand? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$t = \dfrac{2 \times 15}{9.8}$$

Q: A car travels at $$30\ \mathrm{m/s}$$ and then decelerates uniformly to $$10\ \mathrm{m/s}$$ over $$100\ \mathrm{m}. $$What is the acceleration?

$$a = \dfrac{(10^2$ - 30^2$)}{2 \times 100}$$

Q: A person drops a stone from a bridge $$20\ \mathrm{m}$$ above a river. How long does it take to hit the water? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$t = \sqrt{\dfrac{2 \times 20}{9.8}}$$

Question 1

A block slides down a frictionless inclined plane that makes an angle $$	heta$$ with the horizontal. If the acceleration due to gravity is $$g$$, what is the acceleration of the block along the plane?

Accepted Answer

$$g \sin 	heta$$

Question 2

A ball is dropped from rest from a height $$h$$ above the ground. Neglecting air resistance, which equation gives the time $$t it $$takes to reach the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 3

A car accelerates from rest at a constant acceleration $$a$$ for a time $$t. $$What is the distance $$x it $$travels in that time?

Accepted Answer

$$x = \dfrac{1}{2} a t^2$

Question 4

A stone is thrown vertically upward with an initial velocity $$v_0. $$What is the maximum height $$h_{max} it $$reaches above the starting point?

Accepted Answer

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

Question 5

A rock is thrown downward from a cliff with an initial speed $$v_0. $$What is the velocity $$v of $$the rock after falling a distance $$h$$? (Assume downward is positive and neglect air resistance.)

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh}$$

Question 6

A train moves with a constant acceleration. If its initial velocity is $$v_0$$ and after time $$t$$ its velocity is $$v$$, what is the acceleration $$a$$?

Accepted Answer

$$a = \dfrac{v - v_0$}{t}$$

Question 7

A ball is thrown straight up with an initial velocity of $$10\ \mathrm{m/s}. $$How long does it take to reach its maximum height? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$t = \dfrac{10}{9.8}\ \mathrm{s}$$

Question 8

A cyclist starts from rest and accelerates at $$2\ \mathrm{m/s^2$}$$ for $$5$$ seconds. What is the final velocity?

Accepted Answer

$$v = 10\ \mathrm{m/s}$$

Question 9

A skydiver jumps from a plane and falls freely under gravity (neglecting air resistance). Which of the following best describes the motion?

Accepted Answer

Constant downward acceleration of $$g$$

Question 10

A car moving at $$20\ \mathrm{m/s}$$ comes to a stop in $$4$$ seconds with constant acceleration. What is the magnitude of its acceleration?

Accepted Answer

$$5\ \mathrm{m/s^2$}$$

Question 11

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

Accepted Answer

$$t = \sqrt{\dfrac{2 	imes 45}{9.8}}$$

Question 12

A runner accelerates uniformly from $$3\ \mathrm{m/s} to$$ $$9\ \mathrm{m/s}$$ over a distance of $$36\ \mathrm{m}. $$What is the acceleration?

Accepted Answer

$$a = \dfrac{(9^2$ - 3^2$)}{2 	imes 36}$$

Question 13

A package is dropped from a helicopter hovering $$80\ \mathrm{m}$$ above the ground. How fast is it moving just before it hits the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{2 	imes 9.8 	imes 80}$$

Question 14

A skier starts from rest and accelerates down a frictionless slope at $$4\ \mathrm{m/s^2$}. $$How far does the skier travel in $$3$$ seconds?

Accepted Answer

$$x = \dfrac{1}{2} 	imes 4 	imes 3^2$

Question 15

A ball is thrown upward with a velocity of $$15\ \mathrm{m/s}. $$How long does it take to return to the thrower's hand? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$t = \dfrac{2 	imes 15}{9.8}$$

Question 16

A car travels at $$30\ \mathrm{m/s}$$ and then decelerates uniformly to $$10\ \mathrm{m/s}$$ over $$100\ \mathrm{m}. $$What is the acceleration?

Accepted Answer

$$a = \dfrac{(10^2$ - 30^2$)}{2 	imes 100}$$

Question 17

A person drops a stone from a bridge $$20\ \mathrm{m}$$ above a river. How long does it take to hit the water? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$t = \sqrt{\dfrac{2 	imes 20}{9.8}}$$

Question 18

A ball is thrown downward with an initial velocity of $$5\ \mathrm{m/s}$$ from a height of $$25\ \mathrm{m}. $$What is its velocity just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{5^2$ + 2 	imes 9.8 	imes 25}$$

Question 19

A runner accelerates from rest at $$1.5\ \mathrm{m/s^2$}$$ for $$8$$ seconds. What is the total distance covered?

Accepted Answer

$$x = \dfrac{1}{2} 	imes 1.5 	imes 8^2$

Question 20

A ball is thrown straight up with an initial velocity $$v_0. $$Which of the following correctly describes its velocity at the highest point?

Accepted Answer

Zero

Kinematics and Motion on Inclined Planes: Study Notes

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