Acceleration
Physics 11
Acceleration
 similar to how velocity is the rate of change of
position w.r.t. time  determined by the slope
of a line on a position-time graph
 acceleration is the rate of change of velocity
w.r.t. time  the slope of a line on a velocitytime graph
 position time, velocity time and acceleration
time graphs for agiven situation
 are linked
together 
v v  v
a
t

2
1
t 2  t1
Acceleration
  
 v v2  v1
a

t t 2  t1
Graphing
 Plot the following data in a
position time graph
 Determine the
instantaneous velocity at
t = 0.5 s, 2.0 s & 4.0 s
 Use the data to plot a
velocity time graph
 Determine the slope of the
line on the velocity time
graph and use this to plot
an acceleration time graph
Time (s)
Position (cm)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
2.0
3.2
6.9
13.0
21.6
32.7
46.1
62.1
80.5
101.3
124.6
140.0
120.0
Position (cm)
100.0
80.0
60.0
40.0
20.0
0.0
0
1
2
3
Time (s)
4
5
6
60.0
Velocity (cm/s)
50.0
40.0
30.0
20.0
10.0
0.0
0
1
2
3
Time (s)
4
5
6
Acceleration (cm/s^2)
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
1
2
3
Time (s)
4
5
6
Examples of motion diagrams with position
vectors:
An object is at constant or uniform speed if its
displacement vectors are the same length.
Examples of motion diagrams with position
vectors:
An object is slowing down if its displacement
vectors are decreasing in length.
Examples of motion diagrams with position
vectors:
An object is speeding up if its displacement vectors
are increasing in length.
Examples of motion diagrams with velocity
and acceleration vectors:

0
•For constant velocity, vectors are represented by the zero vector, , or
 a dot (no arrow).
•Therefore, the acceleration vectors, , represented by the zero vector, 0 , or a dot (no arrow).
•This is no acceleration or constant velocity. The operational definition is the separation of
position on a motion diagram remains constant in equal time intervals.
Examples of motion diagrams with velocity
and acceleration vectors:
•For an object slowing down at a constant rate, the vectors are the same and point in the opposite

direction to motion. Therefore, the acceleration vectors, a, are the same length but point in the
opposite direction to motion.
•This is constant negative acceleration or slowing down in a positive direction. The operational
definition of constant acceleration in this situation is the separation of position on a motion diagram
decreases by the same amount in equal time intervals.
Examples of motion diagrams with velocity
and acceleration vectors:
•For an object speeding up at a constant rate, the vectors are the same and point in the same

direction as motion. Therefore, the acceleration vectors, a , are the same length and point in the
same direction as motion.
•This is constant positive acceleration or speeding up in a positive direction. The operational
definition of constant acceleration in this situation is the separation of position on a motion diagram
increases by the same amount in equal time intervals.
For motion along a line:
•An object is speeding up if and only if v
and a point in the same direction.
•An object is slowing down if and only if
v and a point in the opposite direction.
•An object’s velocity is constant if and
only if a = 0.
•A positive or negative acceleration DOES
NOT indicate that an object is speeding up or
slowing down.
•A positive acceleration can indicate a slowing
down of an object in a negative direction OR a
speeding up in a positive direction.
•Conversely, a negative acceleration can
indicate a speeding up of an object in a
negative direction OR a slowing down in a
positive direction.
Acceleration
 Acceleration is a vector quantity
 the direction of both the velocity and acceleration is
crucial to understanding the situation




Positive velocity with positive acceleration (faster
to the right/up)
Positive velocity with negative acceleration (slower
to the right/up)
Negative velocity with positive acceleration (slower
to the left/down)
Negative velocity with negative acceleration (faster
to the left/down)
Pictorial Representations
• Graphs are not pictures, but drawing pictures or pictorial
representations that contain important information about
a kinematics situation can provide a greater understanding
of the motion.
•The steps to drawing a pictorial representation are:
1. Draw a motion diagram.
2. Establish coordinate system.
3. Sketch the situation.
4. Define symbols.
5. List knowns and unknowns.
6. Identify desired unknown.
Problem-Solving Steps in Kinematics
1. List known and unknown values and what
value one wishes to find.
2. Draw a pictorial representation.
3. Draw a motion diagram and graphical
representation (if appropriate).
4. Develop a mathematical representation with
formulae using the variables and values in
the pictorial representation. Solve.
5. Assess the result. Is the answer
reasonable? Check for appropriate units
and significant digits.
Practice Problems
 Page 42: #13
 Use Figure 2-27 on page 42 to determine the
average acceleration between t = 10 s & 30 s
 Use Figure 2-27 on page 42 to determine the
average acceleration between t = 70 s & 90 s