Q: A moving hockey puck encounters a patch of rough road and slides 90 cm before coming to a full stop. Assuming a constant deceleration of 8 m/s², what was the puck’s initial speed?

Use $$v^2$$ = $$v_0^2 + 2a$$ \Delta x$$, so v_0$ = \sqrt{2 \times 8 \times 0.9} = 3.8 m/s.$$

Question 1

Which of the following statements best describes the information provided by a position-time graph?

Accepted Answer

It shows position on the y-axis and time on the x-axis.

Question 2

If the slope of a position-time graph is constant and positive, what can be said about the object's motion?

Accepted Answer

The object is moving forward at a constant speed.

Question 3

Given a position-time graph, how do you calculate the average velocity between two points?

Accepted Answer

By calculating $$\frac{\Delta x}{\Delta t}$$ between the two points.

Question 4

A position-time graph is curved upward (smiley face). What does this indicate about the object's acceleration?

Accepted Answer

The object has positive acceleration.

Question 5

On a velocity-time graph, what does the area between the graph and the time axis represent?

Accepted Answer

The object's displacement.

Question 6

A car accelerates from 5 m/s to 21 m/s at a constant 3.0 m/s². How far does it travel while accelerating?

Accepted Answer

Use $$\Delta x = \frac{v^2$ - v_0$^2}{2a}$$, so $$\Delta x = \frac{(21^2$ - 5^2$)}{2 	imes 3} = 68 m.$$

Question 7

A moving hockey puck encounters a patch of rough road and slides 90 cm before coming to a full stop. Assuming a constant deceleration of 8 m/s², what was the puck’s initial speed?

Accepted Answer

Use $$v^2$$ = $$v_0^2 + 2a$$ \Delta x$$, so v_0$ = \sqrt{2 	imes 8 	imes 0.9} = 3.8 m/s.$$

Question 8

A bullet is fired from rest and leaves the barrel at 970 m/s. The barrel is 70.0 cm long. For how long is the bullet accelerated?

Accepted Answer

Use $$v^2$$ = $$v_0^2 + 2a$$ \Delta x$$ to find a$, then t$$ = \frac{v - $$v_0$$}{a}$$; a$$ = \frac{$$970^2$$}{2 	imes 0.7} = 671,428.6$$ m/s², t$$ = \frac{970}{671,428.6} \approx 0.0014$$ s.

Question 9

Which equation is appropriate for calculating displacement when acceleration is constant and initial velocity is not zero?

Accepted Answer

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

Question 10

A rock is thrown upward with a speed of 27.0 m/s from the roof of a 31.0-m-tall building. What is the speed of the rock just before it hits the street?

Accepted Answer

Use $$v^2$$ = $$v_0^2 + 2a$$ \Delta y$$, v$$ = \sqrt{$$27^2 + 2$$ 	imes 9.8 	imes 31} = 44.2$$ m/s.

Question 11

In a velocity-time graph, what does a horizontal line above the time axis indicate?

Accepted Answer

The object is moving forward at constant speed.

Question 12

A police car at rest is passed by a speeder traveling at 36 m/s. The police officer accelerates at 2.00 m/s². How long does it take for the police officer to overtake the speeder?

Accepted Answer

Set $$36t = \frac{1}{2} 	imes 2 t^2$, solve t = 36$ s.

Question 13

Which of the following best describes the relationship between position, velocity, and acceleration graphs?

Accepted Answer

The slope of the position-time graph gives the value of the velocity-time graph, and the slope of the velocity-time graph gives the value of the acceleration-time graph.

Question 14

If an object is speeding up, what must be true about the signs of its velocity and acceleration?

Accepted Answer

They must have the same sign.

Question 15

A subway train starts from rest and accelerates at 1.50 m/s² for 14.0 s, then runs at constant speed for 60.0 s, and finally slows down at 3.50 m/s² until it stops. What is the total distance covered?

Accepted Answer

Calculate each segment: $$\Delta x_1$ = \frac{1}{2} 	imes 1.5 	imes 14^2$ = 147 m$$, $$v = 1.5 	imes 14 = 21 m/s$$, $$\Delta x_2$ = 21 	imes 60 = 1260 m$$, $$\Delta x_3$ = \frac{21^2$}{2 	imes 3.5} = 63 m$$; total $$= 147 + 1260 + 63 = 1470 m.$$

Question 16

In a catch-up problem, what must be true when one object overtakes another?

Accepted Answer

They have the same position at the same time.

Question 17

A ball is dropped from rest from a 100 m-tall building. What is its velocity right before hitting the ground? (Take $$g = 9.8 m/s$$²)

Accepted Answer

Use $$v^2$$ = $$v_0^2 + 2a$$ \Delta y$$, v$$ = \sqrt{2 	imes 9.8 	imes 100} = 44.3$$ m/s.

Motion in One Dimension: Position, Velocity, and Acceleration

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