Question

study lessons 3 and 4 of the 1 - d kinematics chapter at the physics classroom http://www.physicsclassroom.com/class/1dkin/1dkintoc.html
mop connection: kinematic graphing: sublevels 1 - 11 (emphasis on sublevels 9 - 11)

1. the slope of the line on a position vs. time graph reveals information about an objects velocity. the magnitude (numerical value) of the slope is equal to the objects speed and the direction of the slope (upward / + or downward / -) is the same as the direction of the velocity vector. apply this understanding to answer the following questions.

a. a horizontal line means
b. a straight diagonal line means
c. a curved line means
d. a gradually sloped line means
e. a steeply sloped line means

1. the motion of several objects is depicted on the position vs. time graph. answer the following questions. each question may have less than one, one, or more than one answer.

a. which object(s) is(are) at rest?
b. which object(s) is(are) accelerating?
c. which object(s) is(are) not moving?
d. which object(s) change(s) its direction?
e. which object is traveling fastest?
f. which moving object is traveling slowest?
g. which object(s) is(are) moving in the same direction as object b?

1. the slope of the line on a velocity vs. time graph reveals information about an objects acceleration. furthermore, the area under the line is equal to the objects displacement. apply this understanding to answer the following questions.

a. a horizontal line means
b. a straight diagonal line means
c. a gradually sloped line means
d. a steeply sloped line means

1. the motion of several objects is depicted by a velocity vs. time graph. answer the following questions. each question may have less than one, one, or more than one answer.

a. which object(s) is(are) at rest?
b. which object(s) is(are) accelerating?
c. which object(s) is(are) not moving?
d. which object(s) change(s) its direction?
e. which accelerating object has the smallest acceleration?
f. which object has the greatest acceleration?
g. which object(s) is(are) moving in the same direction as object e?

Explanation:

Step1: Analyze position - time graph concepts

On a position - time graph, the slope of the line represents velocity.

a. Horizontal line

A horizontal line has a slope of 0. So, the object is at rest.

b. Straight diagonal line

A straight diagonal line has a constant non - zero slope. So, the object is moving with a constant velocity.

c. Curved line

A curved line means the slope is changing. So, the object is accelerating or decelerating.

d. Gradually sloped line

A gradually sloped line has a small magnitude of slope. So, the object is moving with a slow speed.

e. Steeply sloped line

A steeply sloped line has a large magnitude of slope. So, the object is moving with a fast speed.

Step2: Analyze the position - time graph in question 2

a. At rest

Objects A and E are at rest as their position - time graphs are horizontal lines.

b. Accelerating

Object C is accelerating as its position - time graph is curved.

c. Not moving

Same as at rest, objects A and E are not moving.

d. Change direction

Object C changes direction as the slope of its graph changes sign.

e. Traveling fastest

Object B is traveling fastest as it has the steepest positive slope.

f. Moving slowest

Among moving objects, object D is moving slowest as it has a relatively small positive slope.

g. Same direction as B

Object D is moving in the same direction as B as both have positive slopes.

Step3: Analyze velocity - time graph concepts

On a velocity - time graph, the slope of the line represents acceleration and the area under the line represents displacement.

a. Horizontal line

A horizontal line means the acceleration is 0. So, the object is moving with a constant velocity.

b. Straight diagonal line

A straight diagonal line means the acceleration is constant.

c. Gradually sloped line

A gradually sloped line means the acceleration has a small magnitude.

d. Steeply sloped line

A steeply sloped line means the acceleration has a large magnitude.

Step4: Analyze the velocity - time graph in question 4

a. At rest

No object is at rest as no graph has a zero velocity throughout.

b. Accelerating

Objects B, C, D are accelerating as their graphs have non - zero slopes.

c. Not moving

No object is not moving as no graph has a zero velocity throughout.

d. Change direction

Object C changes direction as its velocity changes sign.

e. Smallest acceleration

Object D has the smallest acceleration as its slope has the smallest magnitude among accelerating objects.

f. Greatest acceleration

Object B has the greatest acceleration as its slope has the largest magnitude.

g. Same direction as E

No object is moving in the same direction as E as E has a negative velocity and others have positive or mixed velocity behavior.

Answer:

1.
a. The object is at rest.
b. The object is moving with a constant velocity.
c. The object is accelerating or decelerating.
d. The object is moving with a slow speed.
e. The object is moving with a fast speed.
2.
a. A, E
b. C
c. A, E
d. C
e. B
f. D
g. D
3.
a. The object is moving with a constant velocity.
b. The object has a constant acceleration.
c. The object has a small acceleration.
d. The object has a large acceleration.
4.
a. None
b. B, C, D
c. None
d. C
e. D
f. B
g. None