The following practice questions test your understanding of the
graphical description of motion. Once answering the questions
#1-13, depress mouse on the "pop-up menu" to view the answer. Use
the "See Explanation" link to view an explanation of the answer.
For questions #14-37, click on the "See Answer" link to view the
answer accompanied by an explanation. Further information is
available on-line at The Physics
Classroom Tutorial.
NOTE to the Student:
There is a lot of information on this page. It is suggested
that you first read the questions and make efforts to answer all
the questions before peeking at the answers. Once you've
answered all the questions, then check your answers. Physics is
learned most effectively when your mind is actively engaged in the
processes of analyzing and predicting. Avoid treating the
information on this page as factual information to be dumped
inside of a mental receptacle. Avoid merely looking at the
answers; take the time to study the logic of the answers. If still
unclear, consider online help at The
Physics Classroom Tutorial or see your teacher for further
assistance.
Use the following graph to answer questions
#1-6.
1. Which object(s) is(are) maintaining a state of motion (i.e.,
maintaining a constant velocity)? See Explanation.
14. Sketch a position-time graph for an object
which is moving with a constant, positive velocity. See
Answer.
15. Sketch a position-time graph for an object
which is moving with a constant, negative velocity. See
Answer.
16. Sketch a position-time graph for an object
moving in the + dir'n and accelerating from a low velocity to a
high velocity. See Answer.
17. Sketch a position-time graph for an object
moving in the + dir'n and accelerating from a high velocity to a
low velocity. See Answer.
18. Sketch a position-time graph for an object
moving in the - dir'n and accelerating from a high velocity to a
low velocity. See Answer.
19. Sketch a position-time graph for an object
moving in the - dir'n and accelerating from a low velocity to a
high velocity. See Answer.
20. Sketch a position-time graph for an object
moving in the + dir'n with constant speed; first a slow constant
speed and then a fast constant speed. See
Answer.
21. Sketch a position-time graph for an object
moving in the + dir'n with constant speed; first a fast constant
speed and then a slow constant speed. See
Answer.
22. Sketch a position-time graph for an object
moving in the - dir'n with constant speed; first a slow constant
speed and then a fast constant speed. See
Answer.
23. Sketch a position-time graph for an object
moving in the - dir'n with constant speed; first a fast constant
speed and then a slow constant speed. See
Answer.
24. Sketch a position-time graph for an object
which moves in the + direction at a slow constant speed and then
in a - direction at a fast constant speed. See
Answer.
25. Sketch a position-time graph for an object
which moves in the + direction at a fast constant speed and then
in a - direction at a slow constant speed. See
Answer.
26. Sketch a position-time graph for an object
which moves in the - direction at a slow constant speed and then
in a + direction at a fast constant speed. See
Answer.
27. Sketch a velocity-time graph for an object
moving with a constant speed in the positive direction. See
Answer.
28. Sketch a velocity-time graph for an object
moving with a constant speed in the negative direction. See
Answer.
29. Sketch a velocity-time graph for an object
which is at rest. See Answer.
30. Sketch a velocity-time graph for an object
moving in the + direction, accelerating from a slow speed to a
fast speed. See Answer.
31. Sketch a velocity-time graph for an object
moving in the + direction, accelerating from a fast speed to a
slow speed. See Answer.
32. Sketch a velocity-time graph for an object
moving in the - direction, accelerating from a slow speed to a
fast speed. See Answer.
33. Sketch a velocity-time graph for an object
moving in the - direction, accelerating from a fast speed to a
slow speed. See Answer.
34. Sketch a velocity-time graph for an object
which first moves with a slow, constant speed in the + direction,
and then with a fast constant speed in the + direction. See
Answer.
35. Sketch a velocity-time graph for an object
which first moves with a fast, constant speed in the + direction,
and then with a slow constant speed in the + direction.
See Answer
36. Sketch a velocity-time graph for an object
which first moves with a constant speed in the + direction, and
then moves with a positive acceleration. See
Answer
37. Sketch a velocity-time graph for an object
which first moves with a constant speed in the + direction, and
then moves with a negative acceleration. See
Answer
Answers and
Explanations
Use the following graph to answer questions #1-6.
1. Objects A, B, D, and E are maintaining a state
of motion (i.e., remaining with constant velocity) as demonstrated
by the constant slope. If the slope is constant, then the velocity
is constant.
2. Object C is accelerating. An acclerating
object has a changing velocity. Since the slope of a p-t graph
equals the velocity, an accelerating object is represented by a
changing slope.
3. Objects A and E are not moving. An object
which is not moving has a zero velocity; this translates into a
line with zero slope on a p-t graph.
4. None of these objects change direction. An
object changes its direction if it changes from a + to a -
velocity (or vice versa). This translates into a p-t graph with a
+ slope and then a - slope (or vice versa).
5. Object B is traveling fastest. To be traveling
fastest is to have the greatest speed (or greatest magnitude of
velocity). This translates into the line on a p-t graph with the
greatest slope.
6. Object D is traveling slowest. To be traveling
slowest is to have the smallest speed (or smallest magnitude of
velocity). This translates into the line on a p-t graph with the
smallest slope.
7. Object C has the greatest acceleration. It is
the only object with an acceleration. Accelerated motion on a p-t
graph is represented by a curved line.
Use the following graph to answer questions #8-13.
8. Objects A and E are maintaining their state of
motion. To maintain the state of motion is to keep a constant
velocity (i.e., to have a zero acceleration). This translates into
a zero slope on a v-t graph.
9. Objects B and C are accelerating (and for a
while, object D). Accelerated motion is indicated by a sloped line
on a v-t graph.
10. Each of the objects are moving. If an object
were not moving, then the v-t graph would be a horizontal line
along the axis (v = 0 m/s).
11. Objects B and C change their direction. An
object that is changing its direction is changing from a + to a -
velocity. Thus, the line on a v-t graph will pass from the + to
the - region of the graph. Object D is not changing its direction;
object D first moves in the - direction with increasing speed and
then maintains a constant speed.
12. Object B has the smallest acceleration.
Acceleration is indicated by the slope of the line. The object
with the smallest acceleration is the object with the smallest
slope.
13. Object A has the greatest velocity (and
object E is a "close second"). The velocity is indicated by how
far above or how far below the axis the line is. Object A has a
large + velocity. Object E has a large (but not as large) -
velocity.
14. A position-time graph for an object which is
moving with a constant, positive velocity is shown below. A
positive, constant velocity is represented by a line with constant
slope (straight) and positive slope (upwards sloping).
15. A position-time graph for an object which is
moving with a constant, negative velocity is shown below. A
negative, constant velocity is represented by a line with constant
slope (straight) and positive slope (upwards sloping).
16. A position-time graph for an object moving
in the + dir'n and accelerating from a low velocity to a high
velocity is shown below. If the object is moving in the + dir'n,
then the slope of a p-t graph would be +. If the object is
changing velocity from small to large values, then the slope must
change from small slope to large slope.
17. A position-time graph for an object moving
in the + dir'n and accelerating from a high velocity to a low
velocity is shown below. If the object is moving in the + dir'n,
then the slope of a p-t graph would be +. If the object is
changing velocity from high to low values, then the slope must
change from high slope to low slope.
18. A position-time graph for an object moving
in the - dir'n and accelerating from a high velocity to a low
velocity is shown below. If the object is moving in the - dir'n,
then the slope of a p-t graph would be -. If the object is
changing velocity from high to low values, then the slope must
change from high slope to low slope.
19. A position-time graph for an object moving
in the - dir'n and accelerating from a low velocity to a high
velocity is shown below. If the object is moving in the - dir'n,
then the slope of a p-t graph would be -. If the object is
changing velocity from low to high values, then the slope must
change from low slope to high slope.
20. A position-time graph for an object moving
in the + dir'n with constant speed; first a slow constant speed
and then a fast constant speed is shown below. If an object is
moving in the + dir'n, then the slope of the line on a p-t graph
would be +. At first, the line has a small slope (corresponding to
a small velocity) and then the line has a large slope
(corresponding to a large velocity).
21. A position-time graph for an object moving
in the + dir'n with constant speed; first a fast constant speed
and then a slow constant speed is shown below. If an object is
moving in the + dir'n, then the slope of the line on a p-t graph
would be +. At first, the line has a large slope (corresponding to
a large velocity) and then the line has a small slope
(corresponding to a small velocity).
22. A position-time graph for an object moving
in the - dir'n with constant speed; first a slow constant speed
and then a fast constant speed is shown below. If an object is
moving in the - dir'n, then the slope of the line on a p-t graph
would be -. At first, the line has a small slope (corresponding to
a small velocity) and then the line has a large slope
(corresponding to a large velocity).
23. A position-time graph for an object moving
in the - dir'n with constant speed; first a fast constant speed
and then a slow constant speed is shown below. If an object is
moving in the - dir'n, then the slope of the line on a p-t graph
would be -. At first, the line has a large slope (corresponding to
a large velocity) and then the line has a small slope
(corresponding to a small velocity).
24. A position-time graph for an object which
moves in the + direction at a slow constant speed and then in a -
direction at a fast constant speed is shown below. The object must
first have a + slope (corresponding to its + velocity) then it
must have a - slope (corresponding to its - velocity). Initially,
the slope is small (corresponding to a small velocity) and then
the slope is large (corresponding to a large velocity).
25. A position-time graph for an object which
moves in the + direction at a fast constant speed and then in a -
direction at a slow constant speed is shown below. The object must
first have a + slope (corresponding to its + velocity) then it
must have a - slope (corresponding to its - velocity). Initially,
the slope is large (corresponding to a large velocity) and then
the slope is small (corresponding to a small velocity).
26. A position-time graph for an object which
moves in the - direction at a slow constant speed and then in a +
direction at a fast constant speed is shown below. The object must
first have a - slope (corresponding to its - velocity) then it
must have a + slope (corresponding to its + velocity). Initially,
the slope is small (corresponding to a small velocity) and then
the slope is large (corresponding to a large velocity).
27. A velocity-time graph for an object moving
with a constant speed in the positive direction is shown below. To
have "a constant speed in the positive direction" is to have a +
velocity which is unchanging. Thus, the line on the graph will be
in the + region of the graph (above 0). Since the velocity is
unchanging, the line is horizontal. Since the slope of a line on a
v-t graph is the object's acceleration, a horizontal line (zero
slope) on a v-t graph is characteristic of a motion with zeo
acceleration (constant velocity).
28. A velocity-time graph for an object moving
with a constant speed in the negative direction is shown below. To
have "a constant speed in the negative direction" is to have a -
velocity which is unchanging. Thus, the line on the graph will be
in the - region of the graph (below 0). Since the velocity is
unchanging, the line is horizontal. Since the slope of a line on a
v-t graph is the object's acceleration, a horizontal line (zero
slope) on a v-t graph is characteristic of a motion with zeo
acceleration (constant velocity).
29. A velocity-time graph for an object which is
at rest is shown below. To be "at rest" is to have a zero
velocity. Thus the line is drawn along the axis (v=0).
30.A velocity-time graph for an object moving in
the + direction, accelerating from a slow speed to a fast speed is
shown below. An object which is moving in the + direction and
speeding up (slow to fast) has a + acceleration. (If necessary,
review the
dir'n of the acceleration vector in the Physics Classroom.)
Since the slope of a line on a v-t graph is the object's
acceleration, an object with + acceleration is represented by a
line with + slope. Thus, the line is a straight diagonal line with
upward (+) slope. Since the velocity is +, the line is plotted in
the + region of the v-t graph.
31.A velocity-time graph for an object moving in
the + direction, accelerating from a fast speed to a slow speed is
shown below. An object whgich is moving in the + direction and
slowing down (fast to slow) has a - acceleration. (If necessary,
review the
dir'n of the acceleration vector in the Physics Classroom.)
Since the slope of a line on a v-t graph is the object's
acceleration, an object with - acceleration is represented by a
line with - slope. Thus, the line is a straight diagonal line with
downward (-) slope. Since the velocity is +, the line is plotted
in the + region of the v-t graph.
32. A velocity-time graph for an object moving
in the - direction, accelerating from a slow speed to a fast speed
is shown below. An object whgich is moving in the - direction and
speeding up (slow to fast) has a - acceleration. (If necessary,
review the
dir'n of the acceleration vector in the Physics Classroom.)
Since the slope of a line on a v-t graph is the object's
acceleration, an object with - acceleration is represented by a
line with - slope. Thus, the line is a straight diagonal line with
downward (-) slope. Since the velocity is -, the line is plotted
in the - region of the v-t graph.
33. A velocity-time graph for an object moving
in the - direction, accelerating from a fast speed to a slow speed
is shown below. An object whgich is moving in the - direction and
slowing down (fast to slow) has a + acceleration. (If necessary,
review the
dir'n of the acceleration vector in the Physics Classroom.)
Since the slope of a line on a v-t graph is the object's
acceleration, an object with + acceleration is represented by a
line with + slope. Thus, the line is a straight diagonal line with
upward (+) slope. Since the velocity is -, the line is plotted in
the - region of the v-t graph.
34. A velocity-time graph for an object which
first moves with a slow, constant speed in the + direction, and
then with a fast constant speed in the + direction is shown below.
Since there are two parts of this object's motion, there will be
two distinct parts on the graph. Each part is in the + region of
the v-t graph (above 0) since the velocity is +. Each part is
horizontal since the velocity during each part is constant
(constant velocity means zero acceleration which means zero
slope). The second part of the graph will be higher since
the velocity is greater during the second part of the motion.
35. A velocity-time graph for an object which
first moves with a fast, constant speed in the + direction, and
then with a slow constant speed in the + direction is shown below.
Since there are two parts of this object's motion, there will be
two distinct parts on the graph. Each part is in the + region of
the v-t graph (above 0) since the velocity is +. Each part is
horizontal since the velocity during each part is constant
(constant velocity means zero acceleration which means zero
slope). The first part of the graph will be higher since
the velocity is greater during the first part of the motion.
36. A velocity-time graph for an object which
first moves with a constant speed in the + direction, and then
moves with a positive acceleration is shown below. Since there are
two parts of this object's motion, there will be two distinct
parts on the graph. Each part is in the + region of the v-t graph
(above 0) since the velocity is +. The slope of the first part is
zero since constant velocity means zero acceleration and zero
acceleration is represented by a horizontal line on a v-t graph
(slope = acceleration for v-t graphs). The second part of the
graph is an upward sloping line since the object has +
acceleration (again, the slope = acceleration for v-t graphs)
37. A velocity-time graph for an object which
first moves with a constant speed in the + direction, and then
moves with a negative acceleration is shown below. Since there are
two parts of this object's motion, there will be two distinct
parts on the graph. Each part is in the + region of the v-t graph
(above 0) since the velocity is +. The slope of the first part is
zero since constant velocity means zero acceleration and zero
acceleration is represented by a horizontal line on a v-t graph
(slope = acceleration for v-t graphs). The second part of the
graph is an downward sloping line since the object has -
acceleration (again, the slope = acceleration for v-t graphs)
