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Investigation 1
Units, Linear Motion, Freely Falling Bodies
In mechanics, the fundamental units on which all other units in mechanics are defined are the units of
LENGTH, MASS, and TIME..
Three systems of units are commonly used in science measurements. They are the MKS (or SI), CGS, and
British Engineering System. The table below shows the names of the units and their abbreviations.
Unit of Length
Unit of Mass
Unit of Time
MKS
meter (m)
kilogram (kg)
second (sec or s)
CGS
centimeter (cm)
gram (g)
second (sec or s)
British Engineering
System
foot (ft)
slugs
second (sec or s)
The following questions deal with linear motion (motion in a straight line) where the object is traveling at
a constant velocity (constant speed), or its average velocity (average speed) is known. The relationships
between distance traveled, speed of travel, and time are:
distance = (constant or average velocity) x time
(constant or average velocity) = distance/time
time = distance/(constant or average velocity)
1.
2.
A car is traveling at a constant 30 miles/hr on Pico Boulevard toward the ocean.
a.
What is the speed of the car?
b.
What is the velocity of the car?
c.
Which quantity is a scalar and which one is a vector. What is the difference between a scalar
and a vector?
A truck is traveling on Ocean Park Boulevard toward the ocean.
a.
If the truck is traveling at a constant velocity of 20 m/s, then how far will the truck travel in 6
seconds?
b.
3.
If the speed of the truck is changing, but its average speed is 20 m/s, then how far will the truck
travel in 6 seconds?
a.
A physics student runs a distance of 100 m in 20 seconds at a constant speed. At what speed was
the student running?
b
A second student starts from rest and then slowly increases her speed until she travels a total
distance of 100 m The total time she takes is 20 seconds. Was she traveling at a constant speed?
What was her average speed?
Note that even though the second student was not traveling at a constant speed, her average speed is
the same at the first student’s constant speed, and therefore they both travel the same distance in the
20 seconds.
4. The sketch shows a ball rolling at constant velocity along a level floor. The ball rolls from the first
position shown to the second position in 1 second. The two positions are 2 feet apart. Sketch the position
of the ball at successive 1-second intervals all the way to the wall (neglect any resistance to the motion).
2 ft
The ball is traveling with a speed of ________________________ when it reaches the wall, and takes a
time of approximately ________________________.
5. The table shows data of the average sprinting speeds of some animals. Make whatever computations
are necessary to complete the table. Be sure to include the units.
Animal
Distance
Cheetah
75 m
Greyhound
160 m
Gazelle
1 km
Turtle
Time
Average Speed
25 m/s
10 s
100 km/hr
30 s
1 cm/s
The following questions deal with accelerated motion. Remember that when the acceleration is constant,
the average velocity can easily be calculated. That is, when the acceleration is constant:
average velocity = (initial velocity + final velocity)/2
Remember how distance, average velocity, and time are related to each other:
distance = average velocity x time
6.
A student driving a car starts from rest and accelerates at a rate of 2 m/s2 for 10 seconds.
When you answer the following questions, note down (for yourself) how and why you performed
the steps that allowed you to arrive at your answer. This will help you remember how to solve the
problem.
a.
What was the initial speed of the car?
b.
What was the speed of the car at the end of the 10 seconds?
c.
What was the average speed of the car during the 10 seconds?
d.
How far did the car travel in the 10 seconds?
7. In the previous problem, the student driving the car now slows down (decelerates) and stops in 20
seconds.
a.
What was the initial speed of the car?
b.
What was the speed of the car at the end of the 20 seconds?
c.
What was the average speed of the car during the 20 seconds?
d.
How far did the car travel in the 20 seconds?
The following question looks again at linear motion with a constant acceleration but in the downward
direction. (Refer to Questions 6 and 7.)
The question in the last column is difficult only because the ball changes direction. In order to figure out
the answers remember that the upward motion is symmetric with the downward motion.
8. In this question you will examine a freely falling body, i.e., the effect of air resistance on the object is
ignored. In each case, the time starts from zero when the ball is dropped or thrown. Take the
acceleration due to gravity to be 10 m/s2 (or 32 ft/s2). Make sure you know what you’re doing and why.
The ball is dropped
How fast (initial
velocity) and in what
direction is the ball
traveling at 0 sec?
How fast and in what
direction is the ball
traveling at 1 sec?
What is the average
speed from 0 to 1
second?
How far (distance) is the
ball from its starting
position at 1 second?
How fast and in what
direction is the ball
traveling at 2 sec?
What is the average
speed from 0 to 2
seconds?
How far (distance) is the
ball from its starting
position at 2 sec?
How fast and in what
direction is the ball
traveling at 4 sec?
What is the average
speed from 0 to 4
seconds?
How far distance) is the
ball from its starting
position at 4 sec?
The ball is thrown
downward at 100 m/s
EXTRA CREDIT
The ball is thrown
upward at 20 m/s