PHYSICS STUDY GUIDE
CHAPTER 3: MOTION WITH CONSTANT ACCELERATION
TOPICS:
 Motion with constant Acceleration
WHAT YOU MUST KNOW







Be able to sketch a situation
Be able to draw a motion diagram
Be able to draw graphs such as:
o Motion Diagram
o Position vs. clock reading
o Velocity vs. clock reading
o Acceleration vs. clock reading
Be able to write mathematical models:
o That describes the position of an object that moves with constant acceleration.
o That describes the velocity of an object that moves with constant acceleration.
o That describes the acceleration of an object that moves with constant acceleration.
Make predictions to find velocities, positions and displacements of an object moving with constant
acceleration.
Understand that in the position vs. clock reading graph the displacement of the object can be found
by subtracting the final and initial position on the position axis.
Understand that in the velocity vs. clock reading graph the displacement of the object can be found
as the area bounded between the graph and the horizontal axis (shape of the trapezoid).
CHAPTER SUMMARY
Motion with constant acceleration is the motion of an object that moves in a straight line and its velocity
changes constantly each second.
PHYSICAL QUANTITIES
ACCELERATION
The change in
velocity of an object,
over the change in
time
vxf - vxi
aX =
tf - ti

Symbol: aX
Type of PQ: Vector
(direction matters)
Units: m/s2
Notes:
o
o
o
Acceleration is the slope of the Velocity vs. Clock reading graph.
Acceleration can be positive or negative.
Acceleration is NOT an indicator of an object slowing down or speeding up.
In motion with constant acceleration we studied 8 representations:
1. Description with words
A battery operated cart accelerates at a constant rate of +1 m/s2. The initial position of the cart is
+2 m and the initial velocity of the cart is 0.5 m/s
2. Sketch the situation
-
The sketch shows:
 The direction of the motion of the object.
 The negative and positive direction
 The initial velocity of the object.
 The initial position of the object.
 The initial clock reading of the object
+
vxi = +0.3 m/s
dxi = +2 m
ti = 0 s
3. Motion diagram
V=
-
v1 v2
v3
+
v4
The motion diagrams shows:
 The object represented as a particle.
 The position of the object each second.
 V arrows
 V arrows
4. Data table
POSITION
dx [m]
CLOCK READING
t [s]
+2.0 m
0s
+2.4 m
1s
+3.0 m
2s
+3.8 m
3s
+4.8 m
4s
+6.0 m
5s
The data table shows:

The position of the object each clock reading.
5. Position vs. clock reading graph
The position vs clock reading graph shows:
POSITION
POSITION VS. CLOCK READING
16
14
12
10
8
6
4
2
0

Shape: Parabola

Initial position = Intercept (the point where
the parabola crosses the vertical axis)

Mathematical model:
dXF = ( ½ · aX · t2 ) + ( vXi · t ) + dXi
0
1
2
3
CLOCK READING
4
5
6. Velocity vs. clock reading graph
The velocity vs clock reading graph shows:
VELOCITY
VELOCITY VS. CLOCK READING
6
5
4
3
2
1
0

Shape: Diagonal straight line.

Slope = acceleration

Mathematical model:
vXF = ( aX · t ) + vXi
0
2
4
6
CLOCK READING
Finding the slope:


Remember, the slope of the graph is the acceleration of the object.
Choose any two points on the graph
 Mathematical model: ax =
 Substitutions aX =
 Answer with units
4.5
vxf - vxi
tf - ti
m
m
- 1.5
s
s
4s - 1 s
aX = 1
m
= s
3s
3
m
s2
 The acceleration of the object is
aX = 1
m
s2
7. Acceleration vs. clock reading graph
The acceleration vs clock reading graph shows:
ACCELERATION
ACCELERATION VS. CLOCK READING
1.2
1
0.8
0.6
0.4
0.2
0

Shape: Horizontal straight line.

Mathematical model:
aX = constant
0
2
4
CLOCK READING
6
8. Mathematical models

The mathematical model for the position vs. clock reading graph is
dXF = ( ½ · aX · t2 ) + ( vXi · t ) + dXi, we substitute the acceleration (aX), the initial
velocity (vxi), and the initial position (dxi):
dxf = (

1
m
· 1 2 ·t2 )+ (0.5 m/s ·t) + 2 m
2
s
The mathematical model for the velocity vs. clock reading graph is vXF = ( aX · t ) + vXi, we
substitute the acceleration (aX), and the initial velocity (vxi).
vxF = (· 1

This mathematical model describes the position
of the object at any given clock reading
m
· t )+ 0.5 m/s
s2
This mathematical model describes the
velocity of the object at any given clock
reading
The mathematical model for the acceleration vs. clock reading graph is ax = constant, we
substitute the acceleration (ax)
aX = constant
This mathematical model describes the acceleration of the
object at any given clock reading
PREDICTIONS


Mathematical models are used to make predictions. In motion with constant velocity we can make
predictions such as HOW FAR (displacement), HOW FAST (Velocity), HOW LONG (time)
To make it easy we transform the mathematical model:
vx =
dxf - dxi
tf - ti
, into a triangle:
vxf - vxi
ACCELERATION
vx
ax t
HOW LONG
HOW LONG
t =
v XF - v Xi
aX
Use this mathematical model to make predictions about
the time it takes an object to reach certain velocity.
VELOCITY AFTER ANY DISPLACEMENT
Use this mathematical model to make predictions:
 When t is not given.
 When you need to find the velocity of the object
after any displacement.
 Do not forget to take the square root at the end
of your calculations
( vXF )2 = ( vXi )2 + ( 2 · aX · dX )
DISPLACEMENT (dx)

There are two ways to find the displacement of an object.
1. Using the Position vs. Clock reading graph:
The displacement is the change in position
POSITION VS. CLOCK READING
1. With an arrow identify the initial position (dxi).
POSITION
2. With an arrow identify the Final position (dxF).
16
14
dxF =12
10
8
dxF =564
2
0
3. With an arrow identify the displacement;
always from (dxi) to (dxF).
dx
0
4. Find the displacement with a mathematical
model:
dx = dXF - dXi
1
2
3
4

dx = 12 m – 5 m

dx = 7 m
5
CLOCK READING
2. Using the velocity vs. Clock reading graph:
The displacement is the area bounded between
the axis and the diagonal straight line (the shape
of a trapezoid).
VELOCITY VS. CLOCK READING
VELOCITY
6
1. With an arrow identify base 1 (vxi).
5
2. With an arrow identify base 2 (vxF).
4
3
3. With a horizontal arrow identify the change in
clock reading (t).
vxF
2
vxi
1
0
0
1
2
t
3
CLOCK READING
4
5
4. Find the displacement with a mathematical
model:
dx = ½ · ( vXF + vXi ) ·t

dx = ½ · (4.5 m/s + 2.5 m/s) · 2 s

dx = 7.0 m