Q: An object starts from rest and moves away from the origin with a constant acceleration for 10 seconds, reaching a position of 50 meters. What is the magnitude of its acceleration?

$$a = \frac{2 \times 50}{10^2$} = 1.0\ \mathrm{m/s^2$}$$

Q: A cannonball is shot straight up and reaches a maximum height of $$18\ \mathrm{m}. $$What was its initial velocity? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$v_0$$ = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 18} = 18.8\ \mathrm{m/s}$$

Q: A car accelerates from $$15\ \mathrm{m/s} to$$ $$25\ \mathrm{m/s}$$ while traveling $$125\ \mathrm{m}$$ south. What is the acceleration?

$$a = \frac{(25^2$ - 15^2$)}{2 \times 125} = 0.8\ \mathrm{m/s^2$}$$

Question 1

An object starts from rest and moves away from the origin with a constant acceleration for 10 seconds, reaching a position of 50 meters. What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{2 	imes 50}{10^2$} = 1.0\ \mathrm{m/s^2$}$$

Question 2

Given the position-time graph for Object A is a curve that gets steeper with time, which of the following best describes the motion?

Accepted Answer

Object A is moving with increasing velocity (accelerating).

Question 3

At $$t = 2\ \mathrm{s}$$, the position of an object is $$x = 8\ \mathrm{m}$$ and at $$t = 3\ \mathrm{s}$$, $$x = 15\ \mathrm{m}. $$What is the average velocity between these times?

Accepted Answer

$$v_{avg} = \frac{15 - 8}{3 - 2} = 7\ \mathrm{m/s}$$

Question 4

A car, initially at rest, accelerates at a constant rate of $$4.0\ \mathrm{m/s^2$}$$ for $$6\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = 0 + (4.0)(6) = 24\ \mathrm{m/s}$$

Question 5

A tailback running at $$5.0\ \mathrm{m/s}$$ slows down at a uniform rate of $$0.25\ \mathrm{m/s^2$}$$ after running an additional $$10\ \mathrm{m}. $$What is his final velocity?

Accepted Answer

$$v^2$$ = $$(5.0)^2 + 2(-0.25)(10$$) \Rightarrow v = 4.36\ \mathrm{m/s}$$

Question 6

Which of the following best describes the velocity-time graph for an object moving with constant acceleration?

Accepted Answer

A straight line with a non-zero slope.

Question 7

A cannonball is shot straight up and reaches a maximum height of $$18\ \mathrm{m}. $$What was its initial velocity? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_0$$ = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 18} = 18.8\ \mathrm{m/s}$$

Question 8

A car accelerates from $$15\ \mathrm{m/s} to$$ $$25\ \mathrm{m/s}$$ while traveling $$125\ \mathrm{m}$$ south. What is the acceleration?

Accepted Answer

$$a = \frac{(25^2$ - 15^2$)}{2 	imes 125} = 0.8\ \mathrm{m/s^2$}$$

Question 9

Ashley is riding her bike at $$3\ \mathrm{m/s}$$ north. Michelle starts to chase her and speeds up to $$5\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is Michelle's acceleration?

Accepted Answer

$$a = \frac{5 - 3}{5} = 0.4\ \mathrm{m/s^2$}$$

Question 10

A ball is released from rest at the top of a ramp. Which motion map best represents its movement?

Accepted Answer

The spacing between position marks increases as the ball accelerates down the ramp.

Question 11

Given two objects A and B, with position-time graphs where A's curve is steeper than B's at $$t = 3\ \mathrm{s}$$, which has the greater instantaneous velocity at that time?

Accepted Answer

Object A

Question 12

A projectile is thrown upward with velocity $$v_0. $$What is its velocity when it returns to the same height from which it was launched (neglecting air resistance)?

Accepted Answer

$$-v_0$

Question 13

A car accelerates at $$2\ \mathrm{m/s^2$}$$ from rest. How far does it travel in $$5\ \mathrm{s}$$?

Accepted Answer

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 2 	imes 25 = 25\ \mathrm{m}$$

Question 14

Eve throws an egg downward from a height of $$30\ \mathrm{m}$$ with an initial velocity of $$5\ \mathrm{m/s}. $$What is the velocity of the egg just before it hits the ground? (Assume $$g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$v^2$$ = $$(5)^2 + 2$$ 	imes 10 	imes 30 \Rightarrow v = \sqrt{25 + 600} = 25\ \mathrm{m/s}$$

Question 15

Which kinematic equation would you use to find displacement when initial velocity, acceleration, and time are known?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 16

If the velocity-time graph of an object is a horizontal line above the time axis, what does this indicate about the object's motion?

Accepted Answer

The object is moving at a constant velocity.

Question 17

A car travels $$100\ \mathrm{m} in$$ $$5\ \mathrm{s}$$, starting from rest and accelerating uniformly. What is its acceleration?

Accepted Answer

$$a = \frac{2 	imes 100}{5^2$} = 8\ \mathrm{m/s^2$}$$

Question 18

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity with respect to time.

Kinematics: Motion, Velocity, and Acceleration Study Guide

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