PART III. KINEMATICS
A. VOCABULARY REVIEWS
On the line, write the term that correctly completes each statement. Use each term once.
1. rise (Δy)
2. time interval
The vertical separation of any two points on a curve
is the ____
The difference between two clock readings is the ____
3. clock reading
A measurement of time is a _____
4. displacement
The change in position of an object is the ____
5. run (Δx)
The horizontal separation of any two points on a curve is
the ____
An object that has the same average velocity for all time
intervals is moving at_____
6. constant velocity
______
7. scalar
A quantity that has only magnitude is a______ quantity.
8. speed
The magnitude of velocity is the ____
9. slope
The ratio of rise to run is the____ of a line of a graph.
10. vector
A ______quantity has both magnitude and direction
11. average velocity
The change of position divided by the time interval
over which the change occurred is the ____
12. acceleration
The change of velocity divided by the time interval
over which the change occurred is the ____
13. average speed
The total distance divided by the total time.
14. initial velocity
The velocity when the clock reading is zero is the ____
15. final velocity
The velocity after acceleration has occurred is the ____
16. acceleration due to gravity (g)
The constant acceleration that acts on falling bodies is _
1
2.
1. velocity
The slope of a position-time graph gives the_____
2. acceleration
The slope of a velocity-time graph gives the_____
3. s
The units of time
4. meter
The units of distance
5. m/s
The units of velocity
6. m/s2
The units of acceleration
7. Newton
The units of force
3.
1. horizontal velocity
Along the path of a projectile the ____
2. magnitude
The size of a quantity is the _________
3. Pythagorean theorem
The ____ is a mathematical method to find the resultant.
4. zero
The vertical velocity at the top of a projectile's path is__
5. components
When a projectile is thrown at an angle, it's initial velocity
has two: ________
Another name given to the horizontal distance is the ____
6. range
___ is constant.
B. MULTIPLE CHOICE
1. Speed is
A)
a measure of how fast something is moving.
B)
the distance covered per unit time.
C)
always measured in terms of a unit of distance divided by a unit of time.
D)
all of the above
2. One possible unit of speed is
A)
miles per hour.
B)
kilometers per hour.
C)
meters per second.
D)
all of the above
2
3. When you look at the speedometer in a moving car, you can see the car’s
A)
instantaneous speed.
B)
average speed.
C)
instantaneous acceleration.
D)
average acceleration.
4. Suppose you take a trip that covers 240 km and takes 4 hours. Your average speed is
A)
480 km/h.
B)
240 km/h.
C)
120km/h.
D)
60 km/h.
5. Acceleration is defined as the change in
A)
position divided by the time interval.
B)
velocity divided by the time interval.
C)
time it takes to move from one speed to another speed.
D)
time it takes to move from one place to another place.
6. Suppose you are in a car that is going around a curve. The speedometer reads a constant
30 miles per hour. Which of the following is NOT true?
A)
You and the car are accelerating.
B)
Your speed is constant.
C)
Your velocity is constant.
D)
Your acceleration is constant.
7. A ball is thrown straight up. At the top of its path its acceleration is
A)
0 m/s2
B)
about 5 m/s2
C)
about 10 m/s2
D)
about 20 m/s2
8. A vector is a quantity that has
A)
magnitude and time.
B)
magnitude and direction.
C)
time and direction.
9. The horizontal component of a projectile’s velocity is independent of
A)
the vertical component of its velocity
B)
the range of the projectile.
C)
time.
10. Which of the following would NOT be considered a projectile?
A)
A cannonball thrown through the air
B)
A cannonball rolling down a slope
C)
A cannonball thrown straight up
D)
A cannonball rolling off the edge of a table
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11. A ball is thrown into the air at some angle between 10 degrees and 90 degrees. At the very
top of the ball’s path, its velocity is
A)
entirely vertical.
B)
entirely horizontal.
C)
both vertical and horizontal.
D)
There’s not enough information given to determine.
C. GRAPHS: In order to get credit please include:
- Title of the graph: Position versus Time, Velocity versus Time
- Label the axes with units: x (m), v (m/s), t (s)
1. Graph the following data on a position-time graph
Position (m)
0
20
40
60
80
100
Time (s)
0
1
2
3
4
5
2. What type of motion is
represented by the graph?
_____ Constant speed
______ Accelerated motion
3. Find the slope of the graph with appropriate units. (20 m/s)
4. What does the slope of a position-time graph represent?
4
5. Using the value found on part 3) graph the velocity vs. time for the 5 seconds.
6. Graph the following data.
Position versus Time
Time Position
(s)
(m)
0
0
1
10
2
40
3
90
4
160
5
250
7. What type of motion is
represented by the graph?
_____ Constant speed
______ Accelerated motion
8. Sketch a qualitative velocity-time graph for this motion:
5
9. Sketch the graph that represents the motion of a car.
a. Position versus Time graph
Car moving in the positive direction
at constant speed
b. Position versus Time graph
Car moving in the positive direction
with positive acceleration
c. Velocity versus Time graph
Car moving in the positive direction
at constant speed
d. Velocity versus Time graph
Car moving in the positive direction
with positive acceleration
e. Acceleration versus Time graph
Car moving in the positive direction
at constant speed
b. Acceleration versus Time graph
Car moving in the positive direction
with positive acceleration
6
10. GRAPHICAL ANALYSIS.
a. Describe in words the motion of the object
from t = 0 - 6.0 s.
25
x (m)
Object stands still for 2 s then moves to the
right at constant speed.
0
5
t (s)
b. Construct a qualitative motion map to describe the motion of the object depicted in the graph
above.
● ●
c. What is the instantaneous velocity of the object at the following times?
i)
t = 1.0 s
Object at rest, v = 0 m/s
ii)
t = 3.0 s (Show your work!)
Slope =
30 − 0
= 7.5 m/s
6−2
d. What is the simple average of these two velocities?
7.5/2 = 3.75 m/s
e. What is the average velocity for the entire interval?
v=
Δx 30 − 0
=
= 5 m/s
Δt
6−0
7
f. Why are these two values different? Which is best to describe the motion of the object?
The second value indicates the average velocity over the entire 6 seconds period.
The second one is better for it covers the entire time interval.
v (m/s)
g. Graphically represent the relationship between velocity and time for the object described.
7.5
0
t (s)
5
h. From your velocity vs. time graph determine the total displacement of the object. Mark your
work on the graph.
A = b h = 4 s (7.5 m/s) = 30 m
11. The position versus time graph below represents the motion of an object.
x
B
A
C
t
D
E
G
F
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a. At what point(s) on the graph is the object moving most slowly? (How do you know?)
B and F, slope of a tangent line at those points is zero.
b. Over what intervals on the graph is the object speeding up? (How do you know?)
Between B and C because slope is negative and object moves to the left
and
Between F and G because slope is positive and object moves to the right
c. Over what intervals on the graph is the object slowing down? (How do you know?)
Between A and B because slope is negative and object moves to the right
and
Between E and F because slope is positive and object moves to the left
d. At what point(s) on the graph above is the object changing direction? (How do you know?)
From A to C motion changes from right to left and from E to G motion changes from left to right
12. A stunt car driver testing the use of air bags drives a car at a constant speed of 25 m/s for a
total of 100 m. He applies his brakes and accelerates uniformly to a stop just as he reaches a wall
50 m away.
a. Sketch qualitative position vs. time and velocity vs time graphs on the next page.
b. Use equations to find:
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i) how long does it take for the car to travel the first 100 m.
t=
x 100
=4 s
=
v 25
ii) how long must the brakes be applied for the car to come to a stop in 50 m.
⎛ vo + v f ⎞
x=⎜
⎟t
2
⎝
⎠
2x
2(50)
t=
=
=4s
vo + v f 25 + 0
d. Now that you know the total time of travel, sketch a quantitative velocity vs time graph.
25
4
8
e. Calculate the acceleration provided by the brakes. Show all your work!
slope =
0 − 25
= 6.25 m/s 2
8−4
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