Name: _______________________
Mr. Kepple
Chapter 2: Questions
1D Kinematics – HW#1
Date: ___________ Period: _____
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.
All tie. The objects all have the same displacement in the
same time interval, therefore they all have the same
average velocity.
(b) Rank the paths according to the average speed of the objects, greatest first. Justify your ranking.
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.
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
X Negative ___ Zero
___
Justify your answer:
At 𝑡
the graph shows the position to be negative
(below the horizontal axis).
(b) Indicate below whether the particle’s velocity is positive, negative, or zero, at…
i.
s
X Positive
___
___ Zero
ii.
___ Negative
Justify your answer:
The slope of a line tangent
to the curve at this point is
positive.
s
___ Positive
X Zero
___
iii.
___ Negative
___ Positive
___ Zero
Justify your answer:
X Negative
___
Justify your answer:
The slope of a line tangent
to the curve at this point is
zero.
(c) How many times does the particle go through the point
s
The slope of a line tangent
to the curve at this point is
negative.
? Justify your answer.
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.
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
X West
___
___ Rest
Justify your answer:
The initial direction of travel is indicated by the sign of
the velocity at 𝑡
which is negative (west).
(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.
X East
___
X Yes
___
___ West
___ Rest
___ No
Justify your answer:
Justify your answer:
The final direction of travel is indicated
by the sign of the velocity at end of the
curve which is positive (east).
The velocity is zero on the horizontal
axis and the object crosses the
horizontal axis once.
(d) Indicate whether the acceleration is
positive, negative, or zero.
(e) Indicate whether the acceleration is
constant or varying.
X Positive
___
___
X Constant ___ Varying
___ Negative ___ Zero
Justify your answer:
Justify your answer:
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.
4. The figure gives the velocity of a particle moving along an axis.
(a) Indicate below whether the direction of travel at time
east, west, or if the particle is at rest.
___
X East
___ West
is
___ Rest
Justify your answer:
The direction of travel is indicated by the sign of the
velocity at 𝑡
which is positive (east).
(d) Indicate below whether the direction of
travel at point 4 is east, west, or at rest.
___ East
___
X West
___ Rest
Justify your answer:
The direction of travel is indicated by the
sign of velocity which is negative at
𝑡 4 s.
(e) Rank the six points according to the
magnitude of the acceleration, greatest first.
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.
Name: _______________________
Mr. Kepple
Motion Graphs – Part 1
1D Kinematics – HW#2
𝑣
Date: ___________ Period: _____
+𝑣
−𝑣
REST
rest
𝑡
UM
−𝑎
UM
+𝑎
UM
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!
A to C
C to F
C and F to G
(d) undergoing positive
acceleration? Label it!
(e) undergoing negative
acceleration? Label it!
(f) undergoing uniform
motion? Label it!
E to F
B to D
A to B, D to E,
and F to G
(g) speeding up? Label it!
C to D
(h) slowing down? Label it!
B to C and E to F
𝑣
𝑡
2. Which point or points on the graph – if any – show instants at which there was…
(a) Uniform motion in the
positive direction?
1
(d) Positive acceleration with
positive velocity?
none
(g) Negative acceleration
with negative velocity?
4
(b) Uniform motion in the
negative direction?
5
(e) Positive acceleration with
negative velocity?
6
(h) Zero velocity and
negative acceleration?
3
(c) Rest?
3 and 7
(f) Negative acceleration with
positive velocity?
2
(i) Zero velocity and positive
acceleration?
none
+𝑣
REST
−𝑣
rest
UM
+𝑎
−𝑎
UM
UM
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…
(a) traveling in the positive
direction? Label it!
(b) traveling in the negative
direction? Label it!
B to E
E to G
(d) undergoing positive
acceleration? Label it!
(e) undergoing negative
acceleration? Label it!
B to C
D to F
(g) speeding up? Label it!
B to C and E to F
(h) slowing down? Label it!
(c) at rest? Label it!
A to B and E
(f) undergoing uniform
motion? Label it!
A to B, C to D,
and F to G
D to E
4. 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?
3
7
(d) Positive acceleration with
positive velocity?
2
(g) Negative acceleration
with negative velocity?
6
(e) Positive acceleration with
negative velocity?
none
(h) Zero velocity and
negative acceleration?
5
(c) Rest?
1 and 5
(f) Negative acceleration with
positive velocity?
4
(i) Zero velocity and positive
acceleration?
none
Name: _______________________
Mr. Kepple
Motion Graphs – Part 2
1D Kinematics – HW#3
𝑣
Date: ___________ Period: _____
+𝑣
−𝑣
−𝑣
rest
+𝑣
rest
+𝑎
−𝑎
rest
+𝑎
UM
+𝑎
𝑡
UM
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!
1-3, 9-12
0-1, 3-9
(d) undergoing positive
acceleration? Label it!
(e) undergoing negative
acceleration? Label it!
0-2, 4-6, 8-10
2-4
(g) speeding up? Label it!
(h) slowing down? Label it!
1-2, 3-4, 9-10
0-1, 2-3, 4-6, 8-9
(c) at rest? Label it!
1, 3, 9
(f) undergoing uniform
motion? Label it!
6-8, 10-12
𝑣
𝑡
2. Which point or points on the graph – if any – show instants at which there was…
(a) Uniform motion in the
positive direction?
G
(d) Positive acceleration with
positive velocity?
F
(g) Negative acceleration
with negative velocity?
C
(b) Uniform motion in the
negative direction?
E
(e) Positive acceleration with
negative velocity?
D
(h) Zero velocity and
negative acceleration?
none
(c) Rest?
A
(f) Negative acceleration with
positive velocity?
B
(i) Zero velocity and positive
acceleration?
A
𝑥
−𝑣
+𝑣
REST
rest
𝑡
−𝑎
+𝑎
UM
−𝑎
UM
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…
(a) traveling in the positive
direction? Label it!
(b) traveling in the negative
direction? Label it!
4-10
0-4
(d) undergoing positive
acceleration? Label it!
(e) undergoing negative
acceleration? Label it!
2-6
0-2, 8-10
(g) speeding up? Label it!
(h) slowing down? Label it!
0-2, 4-6
2-4, 8-10
(c) at rest? Label it!
4, 10-12
(f) undergoing uniform
motion? Label it!
6-8, 10-12
𝑥
𝑡
4. 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?
E
none
(d) Positive acceleration with
positive velocity?
D
(g) Negative acceleration
with negative velocity?
A
(e) Positive acceleration with
negative velocity?
B
(h) Zero velocity and
negative acceleration?
none
(c) Rest?
C and G
(f) Negative acceleration with
positive velocity?
F
(i) Zero velocity and positive
acceleration?
C
Mr. Kepple
Name: _______________________
Kinematics and Calculus FRQ
1D Kinematics – HW#4
Date: ___________ Period: _____
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.
𝑑
𝑣(𝑡)
𝑑𝑡
𝑎(𝑡)
𝑑
(
𝑑𝑡
𝑡)
𝑎(𝑡)
(b) Determine the position of the object as a function of time.
𝑥(𝑡)
𝑥( )
𝑣(𝑡)𝑑𝑡
2(
𝑥(𝑡)
𝑡
𝑡 +𝐶
𝑥(𝑡)
𝑡
𝑡2 + 1
( )
𝑡)𝑑𝑡
𝐶
(c) Calculate the initial position and the initial velocity of the object.
𝑥( )
𝑥0
( )2 + 1
( )
1 m
𝑣( )
𝑣0
( )
m/s
(d) At what time does the object reach its maximum position?
Position is at its maximum when the velocity is zero.
𝑣(𝑡)
𝑡
5s
(𝑡)
( )2 + 𝐶
8+𝐶
1 m
(e) Calculate the maximum position the object reaches.
𝑡2 + 1
𝑥(𝑡)
𝑡
𝑥(5)
(5)
𝑥
(5)2 + 1
6 m
(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
𝑥0
1 m
𝑂
𝑡
𝑣
𝑣0
m/s
𝑂
𝑡
𝑎
𝑂
𝑎
m/s2
𝑡