Q: A car's velocity changes from $$4\ \text{m/s} to$$ $$24\ \text{m/s} in$$ $$5\ \text{s}. $$What is its acceleration?

$$a = \dfrac{24 - 4}{5} = 4\ \text{m/s}^2$$

Q: A ball is dropped from rest. What is its speed after $$4\ \text{s}$$, assuming $$g = 10\ \text{m/s}^2$$ and downward is positive?

$$v = gt = 10 \times 4 = 40\ \text{m/s}$$

Q: How far does a dropped ball fall in $$2\ \text{s}$$, starting from rest and neglecting air resistance?

$$d = \dfrac{1}{2}gt^2$ = \dfrac{1}{2} \times 10 \times 2^2$ = 20\ \text{m}$$

Q: A car slows from $$25\ \text{m/s} to$$ $$5\ \text{m/s} in$$ $$4\ \text{s}. $$What is its acceleration?

$$a = \dfrac{5 - 25}{4} = -5\ \text{m/s}^2$$

Q: At the highest point of a ball thrown straight upward, which statement is correct?

Velocity is $$0$$, but acceleration is $$10\ \text{m/s}^2$$ downward.

Q: On a velocity-time graph, velocity increases from $$10\ \text{m/s} at$$ $$2\ \text{s} to$$ $$30\ \text{m/s} at$$ $$6\ \text{s}. $$What is the acceleration?

$$a = \dfrac{30 - 10}{6 - 2} = \dfrac{20}{4} = 5\ \text{m/s}^2$$

Q: A rock is dropped from a bridge and hits the water $$3\ \text{s}$$ later. Estimate the height of the bridge.

$$d = \dfrac{1}{2}gt^2$ = \dfrac{1}{2} \times 10 \times 3^2$ = 45\ \text{m}$$

Q: A ball is thrown upward at $$20\ \text{m/s}. $$Approximately how long does it take to reach the top?

$$t = \dfrac{v_i}{g} = \dfrac{20}{10} = 2\ \text{s}$$

Q: Which of the following best describes the acceleration of an object moving in a straight line at constant velocity?

Acceleration is $$0\ \text{m/s}^2.$$

Q: A steel ball is dropped from rest. What is its velocity after $$4.5\ \text{s}$$, using $$g = 10\ \text{m/s}^2$$?

$$v = gt = 10 \times 4.5 = 45\ \text{m/s}$$

Question 1

A car's velocity changes from $$4\ 	ext{m/s} to$$ $$24\ 	ext{m/s} in$$ $$5\ 	ext{s}. $$What is its acceleration?

Accepted Answer

$$a = \dfrac{24 - 4}{5} = 4\ 	ext{m/s}^2$$

Question 2

A ball is dropped from rest. What is its speed after $$4\ 	ext{s}$$, assuming $$g = 10\ 	ext{m/s}^2$$ and downward is positive?

Accepted Answer

$$v = gt = 10 	imes 4 = 40\ 	ext{m/s}$$

Question 3

How far does a dropped ball fall in $$2\ 	ext{s}$$, starting from rest and neglecting air resistance?

Accepted Answer

$$d = \dfrac{1}{2}gt^2$ = \dfrac{1}{2} 	imes 10 	imes 2^2$ = 20\ 	ext{m}$$

Question 4

A car slows from $$25\ 	ext{m/s} to$$ $$5\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is its acceleration?

Accepted Answer

$$a = \dfrac{5 - 25}{4} = -5\ 	ext{m/s}^2$$

Question 5

At the highest point of a ball thrown straight upward, which statement is correct?

Accepted Answer

Velocity is $$0$$, but acceleration is $$10\ 	ext{m/s}^2$$ downward.

Question 6

On a velocity-time graph, velocity increases from $$10\ 	ext{m/s} at$$ $$2\ 	ext{s} to$$ $$30\ 	ext{m/s} at$$ $$6\ 	ext{s}. $$What is the acceleration?

Accepted Answer

$$a = \dfrac{30 - 10}{6 - 2} = \dfrac{20}{4} = 5\ 	ext{m/s}^2$$

Question 7

A rock is dropped from a bridge and hits the water $$3\ 	ext{s}$$ later. Estimate the height of the bridge.

Accepted Answer

$$d = \dfrac{1}{2}gt^2$ = \dfrac{1}{2} 	imes 10 	imes 3^2$ = 45\ 	ext{m}$$

Question 8

A ball is thrown upward at $$20\ 	ext{m/s}. $$Approximately how long does it take to reach the top?

Accepted Answer

$$t = \dfrac{v_i}{g} = \dfrac{20}{10} = 2\ 	ext{s}$$

Question 9

Which of the following best describes the acceleration of an object moving in a straight line at constant velocity?

Accepted Answer

Acceleration is $$0\ 	ext{m/s}^2.$$

Question 10

A steel ball is dropped from rest. What is its velocity after $$4.5\ 	ext{s}$$, using $$g = 10\ 	ext{m/s}^2$$?

Accepted Answer

$$v = gt = 10 	imes 4.5 = 45\ 	ext{m/s}$$

Question 11

If a ball is thrown upward and reaches its highest point, what is its velocity and acceleration at that instant?

Accepted Answer

Velocity is $$0$$, acceleration is $$10\ 	ext{m/s}^2$$ downward.

Question 12

A ball is dropped from rest. After $$2\ 	ext{s}$$, what is its velocity and how far has it fallen?

Accepted Answer

Velocity: $$v = gt = 20\ 	ext{m/s}$$; Distance: $$d = \dfrac{1}{2}gt^2$ = 20\ 	ext{m}$$

Question 13

A car accelerates from $$0\ 	ext{m/s} to$$ $$30\ 	ext{m/s} in$$ $$6\ 	ext{s}. $$What is the distance covered during this time?

Accepted Answer

$$d = v_i t + \dfrac{1}{2} a t^2$ = 0 + \dfrac{1}{2} 	imes 5 	imes 6^2$ = 90\ 	ext{m}$$

Question 14

A ball is thrown upward at $$15\ 	ext{m/s}. $$How long until it returns to its starting point (neglecting air resistance)?

Accepted Answer

$$t = 2 	imes \dfrac{v_i}{g} = 2 	imes \dfrac{15}{10} = 3\ 	ext{s}$$

Question 15

Which statement about free fall is correct when air resistance is neglected?

Accepted Answer

Heavy and light objects fall with the same acceleration.

Question 16

A ball is thrown downward at $$5\ 	ext{m/s}$$ from a height. What is its speed after $$2\ 	ext{s}$$?

Accepted Answer

$$v_f = v_i + at = 5 + 10 	imes 2 = 25\ 	ext{m/s}$$

Question 17

A ball is thrown upward at $$10\ 	ext{m/s}. $$What is its maximum height?

Accepted Answer

$$d = \dfrac{v_i^2$}{2g} = \dfrac{10^2$}{2 	imes 10} = 5\ 	ext{m}$$

Question 18

A car moves around a curve at constant speed. Which statement is true?

Accepted Answer

The car is accelerating because its velocity direction changes.

Physics with Calculus: Acceleration and Free Fall Study Guidance

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