Motion in One Dimension

1
Chapter 2

• Motion in One Dimension
• (A straight line)

2
Displacement, Time, Average Velocity
x-axis
x 0
x -1
x 1
Direction matters!
Average velocity over a long period of time
3
What does v vs. t look like?
Distance vs. time
4
acceleration Any change in either speed or
direction
Average acceleration
Units are velocity/second m/s2
5
Distance vs. time
v vs. t
What does a vs. t look like?
6
Which represents a car that is moving to the
right at constant speed?

• A
• B
• C
• D
• E
• F
• B and D
• A, B and D
• None of these

7
Distance vs. time
At which point is car 2 turning around and
heading in the opposite direction?
8
Which represents a car that is moving to the
left, slowing to a stop?

• A
• B
• C
• D
• E
• F
• C and F
• A, B and D
• None of these

9
Position vs. time
At which point is the velocity the greatest?

• P
• Q
• R
• S
• Q and S
• Not enough info is given

10
Equations relating x, v, a (aconstant)
11
The human body can only survive accelerations of
less than about 25 gs, which is about 250 m/s2.
If you are in a car crash with an initial speed
of 100 km/h and are stopped by an airbag that
inflates from the dashboard, over what distance
must the airbag stop you for you to survive the
crash?
1. What info do they give?
a 250 m/s2
2. What do they want us to find? Distance
3. Which equation do I use?
1.55 m
12
Free Fall a constant, negative

• A strobe light flashes at constant t as the ball
  is dropped.
• the space between images increases as the balls
  velocity grows.

13
Q2.4
You toss a ball straight upward, in the positive
direction. The ball falls freely under the
influence of gravity. At the highest point in the
balls motion,
A. its velocity is zero and its acceleration is
zero. B. its velocity is zero and its
acceleration is positive (upward). C. its
velocity is zero and its acceleration is negative
(downward). D. its velocity is positive (upward)
and its acceleration is zero. E. its velocity is
positive (upward) and its acceleration is zero.
14
Q2.2
This is the xt graph of the motion of a
particle. Of the four points P, Q, R, and S, the
speed is greatest at
A. point P. B. point Q. C. point R. D. point
S. E. not enough information in the graph to
decide
15
Q2.3
This is the xt graph of the motion of a
particle. Of the four points P, Q, R, and S, the
acceleration ax is greatest (most positive) at
A. point P. B. point Q. C. point R. D. point
S. E. not enough information in the graph to
decide
16
Q2.6
This is a motion diagram of an object moving
along the xdirection with constant acceleration.
The dots 1, 2, 3, show the position of the
object at equal time intervals ?t.
5
4
3
2
1
x
x 0
Which of the following vxt graphs best matches
the motion shown in the motion diagram?
vx
vx
vx
vx
vx
t
t
t
t
t
0
0
0
0
0
A.
B.
C.
D.
E.
17
Q2.7
This is a motion diagram of an object moving
along the xdirection with constant acceleration.
The dots 1, 2, 3, show the position of the
object at equal time intervals ?t.
5
4
3
2
1
x
x 0
Which of the following axt graphs best matches
the motion shown in the motion diagram?
ax
ax
ax
ax
ax
t
t
t
t
t
0
0
0
0
0
A.
B.
C.
D.
E.
18
Q2.8
An object moves along the xaxis with constant
acceleration. The initial position x0 is
positive, the initial velocity is negative, and
the acceleration is positive. Which of the
following vxt graphs best describes this motion?
vx
vx
vx
vx
vx
t
t
t
t
t
0
0
0
0
0
A.
B.
C.
D.
E.
19
Q2.11
The position of an object moving along the x-axis
is given by x 5.0 m (4.0 m/s)t (2.0
m/s2)t2 Which statement about this object is
correct?
A. For t gt 0, the object is never at rest. B. The
object is at rest at t 0.5 s. C. The object is
at rest at t 1.0 s. D. The object is at rest
at t 2.0 s. E. More than one of B., C., and D.
is correct.
20
Q2.12
The position of an object moving along the x-axis
is given by x 5.0 m (4.0 m/s)t (2.0
m/s2)t2 How many times does this object pass
through the point x 0?
A. twice, first moving in the positive
x-direction, then moving in the negative
x-direction B. twice, first moving in the
negative x-direction, then moving in the positive
x-direction C. only once, moving in the positive
x-direction D. only once, moving in the negative
x-direction E. never