Physics Chapter 2 Study Guide
Motion in One Dimension
Distance is
the distance traveled by an object. It is not a vector, but only how far
an object has moved.
Displacement is
the change in position. This similar to the distance traveled, but has
a direction. Displacement IS A VECTOR.
Speed is
the distance traveled divided by the time it took to travel that distance.
Speed is not a vector.
Velocity is
the change in position divided by the change in time. Average velocity is
the total displacement divided by the time interval during which the displacement
occurred. Velocity IS A VECTOR.
Acceleration is
the rate of change of velocity. Acceleration IS A VECTOR.
We have looked at three different graphs
this chapter. The three graphs are a distance-time graph, a velocity-time
graph and an acceleration-time graph. All of the graphs are related to each
other. The graphic below shows what is needed to be calculated to go from
one graph to the other.
Signs of Velocity and Acceleration
a positive
v positive |
Faster in positive x direction |
a negative
v positive |
Slower in positive x direction |
a positive
v negative |
Slower in negative x direction |
a negative
v negative |
Faster in negative x direction |
Kinematics Equations
Kinematics Equations |
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Example 1
A student drives from school to home at
an average speed of 25.3 km/hr. If it takes 4.72 hr. to get to her destination,
how far did she travel?
Example 2
A bicyclist pedaling along a straight road
at 25.0 km/hr uniformly accelerates at 
for
3.00 s. Find her final speed.
Example 3
A classic 12-cylinder Jaguar can go from
rest to 48.3 km/hr in 3.8 s, accelerating uniformly at a rate of 
.
Find its average speed and the distance traveled.
Example 4
You drive a beat-up pickup truck along a
straight road for 8.4 km at 70 km/h, at which point the truck runs out of gasoline
and stops. Over the next 30 minutes, you walk another 2.0 km farther along
the road to a gasoline station.
a) What is your overall displacement from
the beginning of your drive to your arrival at the station?
b) What is the time interval 
from
the beginning of your drive to your arrival at the station?
c) What is your average velocity 
from
the beginning of your drive to your arrival at the station? Find it both numerically
and graphically.
d) Suppose that to pump the gasoline, pay
for it, and walk back to the truck takes you another 45 minutes. What is your
average speed from the beginning of your drive to your return to the truck
with the gasoline?
Free-Fall
Free-Fall occurs
when an object is dropped. The following table shows the velocity and distance
of an object dropped from a height.
Time (s) |
Velocity (m/s) |
Distance (m) |
0 |
0 |
0 |
1 |
10 |
5 |
2 |
20 |
20 |
3 |
30 |
45 |
4 |
40 |
80 |
5 |
50 |
125 |
6 |
60 |
180 |
7 |
70 |
245 |
t |
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Example 5
On September 26, 1993, Dave Munday went
over the Canadian edge of Niagara Falls in a steel ball equipped with an air
hole and then fell 48 m to the water (and rocks). Assume his initial velocity
was zero, and neglect the effect of the air on the ball during the fall.
a) How long did Munday fall to reach the
water surface?
b) Munday could count off the three seconds
fo free fall but could not see how far he had fallen with each count. Determine
his position at each full second.
c) What was Munday's velocity as he reached
the water surface?
d) What was Munday's velocity at each count
of one full second? Was he aware of his increasing speed?
Example 6
A pitcher tosses a baseball up along a y
axis, with an initial speed of 12 m/s.
a) How long does the ball take to reach
its maximum height?
b) What is the ball's maximum height above
its release point?
c) How long does the ball take to reach
a point 5.0 m above its release point?
