Chapter 2: Questions Mr. Kepple · starting point to a final point, all in the same time interval. The paths pass over a grid of equally spaced straight lines. (a) Rank the paths

Chapter 2: Questions 1D Kinematics – HW#1

1. The figure shows four paths along which objects move from a starting point to a final point, all in the same time interval. The paths pass over a grid of equally spaced straight lines.

(a) Rank the paths according to the average velocity of the objects, greatest first. Justify your ranking. (b) Rank the paths according to the average speed of the objects, greatest first. Justify your ranking. 2. The figure to the right is a graph of a particle’s position along an axis versus time. (a) Indicate below whether the sign of the particle’s position at is positive, negative, or zero.

___ Positive ___ Negative ___ Zero

Justify your answer:

(b) Indicate below whether the particle’s velocity is positive, negative, or zero, at…

i. s ii. s iii. s

___ Positive ___ Negative ___ Positive ___ Negative ___ Positive ___ Negative ___ Zero ___ Zero ___ Zero

Justify your answer: Justify your answer: Justify your answer:

(c) How many times does the particle go through the point ? Justify your answer.

Name: _______________________

Date: ___________ Period: _____

All tie. The objects all have the same displacement in the

same time interval, therefore they all have the same

average velocity.

X

4, 1 and 2, then 3. Since all of the objects moved over an equal time interval, the object

that travels the greatest distance will have the greatest average speed.

At 𝑡 the graph shows the position to be negative

(below the horizontal axis).

X X

X

The slope of a line tangent

to the curve at this point is

positive.



zero.



negative.

The position 𝑥 is indicated on the graph by the horizontal axis. We can see that the

curve crosses the horizontal axis twice: once at 𝑡 s and again at 𝑡 s.

Mr. Kepple

3. The figure gives the velocity of a particle moving on an axis.

(a) Indicate below whether the initial direction of travel is east, west, or if the particle is at rest.

___ East ___ West ___ Rest


(a) Indicate below whether the final direction of travel is east, west, or if the particle is at rest.

(c) Indicate below whether the particle is ever at rest.

___ East ___ West ___ Rest ___ Yes ___ No

Justify your answer: Justify your answer:

(d) Indicate whether the acceleration is positive, negative, or zero.

(e) Indicate whether the acceleration is constant or varying.

___ Positive ___ Negative ___ Zero ___ Constant ___ Varying

Justify your answer: Justify your answer: 4. The figure gives the velocity of a particle moving along an axis.

(a) Indicate below whether the direction of travel at time is east, west, or if the particle is at rest.


Justify your answer: (d) Indicate below whether the direction of travel at point 4 is east, west, or at rest.

(e) Rank the six points according to the magnitude of the acceleration, greatest first.



X

The initial direction of travel is indicated by the sign of

the velocity at 𝑡 which is negative (west).

X

The final direction of travel is indicated

by the sign of the velocity at end of the

curve which is positive (east).

X

The velocity is zero on the horizontal

axis and the object crosses the

horizontal axis once.

X

The acceleration of the object is

indicated by the slope of the curve

which is positive.

The velocity curve is linear which

indicates that the acceleration is

constant.

X

X

The direction of travel is indicated by the sign of the

velocity at 𝑡 which is positive (east).

X

The direction of travel is indicated by the

sign of velocity which is negative at

𝑡 4 s.

2 and 6 tie, then 3 and 5 tie, then 1 and 4

tie. The acceleration is found from the

slope of the tangent to the curve,

therefore the points with the greatest

acceleration have the greatest slope.

Motion Graphs – Part 1 1D Kinematics – HW#2

1. The plot above shows the velocity vs. time of a particle. Indicate the interval over which the particle experiences the specified motion and then label that interval on the graph. When is the particle…

(a) traveling in the positive direction? Label it!

(b) traveling in the negative direction? Label it!

(c) at rest? Label it!

(d) undergoing positive acceleration? Label it!

(e) undergoing negative acceleration? Label it!

(f) undergoing uniform motion? Label it!

(g) speeding up? Label it! (h) slowing down? Label it! 2. Which point or points on the graph – if any – show instants at which there was…

(a) Uniform motion in the positive direction?

(b) Uniform motion in the negative direction?

(c) Rest?

(d) Positive acceleration with positive velocity?

(e) Positive acceleration with negative velocity?

(f) Negative acceleration with positive velocity?

(g) Negative acceleration with negative velocity?

(h) Zero velocity and negative acceleration?

(i) Zero velocity and positive acceleration?

Name: _______________________

Date: ___________ Period: _____

𝑣

𝑡

𝑣

𝑡

A to C C to F C and F to G

E to F B to D A to B, D to E, and F to G

C to D B to C and E to F

1 5 3 and 7

none 6 2

4 3 none

rest

+𝑣 −𝑣 REST

UM −𝑎 UM +𝑎 UM

Mr. Kepple

3. The plot above shows the position vs. time of a particle. Indicate the interval over which the particle experiences the specified motion and then label that interval on the graph. When is the particle…










(c) Rest?







B to E E to G A to B and E

B to C D to F A to B, C to D, and F to G

B to C and E to F D to E

3 7 1 and 5

2 none 4

6 5 none

rest

+𝑣 REST −𝑣

UM +𝑎 UM −𝑎 UM

Motion Graphs – Part 2 1D Kinematics – HW#3

1. The plot above shows the velocity vs. time of a particle. Indicate the interval over which the particle experiences the specified motion and then label that interval on the graph. When is the particle…










(c) Rest?







Name: _______________________

Date: ___________ Period: _____

𝑡

𝑣

𝑣

𝑡

1-3, 9-12 0-1, 3-9 1, 3, 9

0-2, 4-6, 8-10 2-4 6-8, 10-12

1-2, 3-4, 9-10 0-1, 2-3, 4-6, 8-9

G E A

F D B

C none A

rest rest rest

−𝑣 +𝑣 −𝑣 +𝑣

+𝑎 −𝑎 +𝑎 UM +𝑎 UM

Mr. Kepple

3. The plot above shows the position vs. time of a particle. Indicate the interval over which the particle experiences the specified motion and then label that interval on the graph. When is the particle…










(c) Rest?







𝑥

𝑡

𝑥

𝑡

4-10 0-4 4, 10-12

2-6 0-2, 8-10 6-8, 10-12

0-2, 4-6 2-4, 8-10

E none C and G

D B F

A none C

rest

−𝑣

−𝑎

+𝑣 REST

+𝑎 UM −𝑎 UM

Kinematics and Calculus FRQ 1D Kinematics – HW#4

An object is moving along the -axis in a region where its velocity as a function of time is given as ( ) , where is in seconds and is in meters per second. When s, the object is observed to be at position 44 meters. (a) Determine the acceleration of the object as a function of time. (b) Determine the position of the object as a function of time. (c) Calculate the initial position and the initial velocity of the object. (d) At what time does the object reach its maximum position?

Name: _______________________

Date: ___________ Period: _____

Position is at its maximum when the velocity is zero.

𝑎(𝑡) 𝑑

𝑑𝑡𝑣(𝑡)

𝑑

𝑑𝑡( 𝑡)

𝑎(𝑡)

𝑥(𝑡) 𝑣(𝑡)𝑑𝑡

( 𝑡)𝑑𝑡𝑥(𝑡) 𝑡 𝑡2 + 𝐶

𝑥( ) ( ) ( )2 + 𝐶

8 + 𝐶

𝐶 1 m

𝑥(𝑡) 𝑡 𝑡2 + 1

𝑥( ) ( ) ( )2 + 1

𝑥0 1 m

𝑣( ) ( )

𝑣0 m/s

𝑣(𝑡) (𝑡)

𝑡 5 s

Mr. Kepple

(e) Calculate the maximum position the object reaches. (f) On the axes below, sketch graphs of the object’s position , velocity , and acceleration as functions of time . The three graphs should cover the same time interval and use the same scale on the horizontal axis. Be sure to label the initial velocity of each quantity.

𝑥

𝑡 𝑂

𝑣

𝑡 𝑂

𝑎

𝑡 𝑂

𝑥0 1 m

𝑥(5) (5) (5)2 + 1

𝑥(𝑡) 𝑡 𝑡2 + 1

𝑥 6 m

𝑣0 m/s

𝑎 m/s2

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Chapter 2: Questions Mr. Kepple · starting point to a final point, all in the same time interval. The paths pass over a grid of equally spaced straight lines. (a) Rank the paths