Graphical Analysis of Motion
Objectives
•  Plot and interpret distance-time and speed-time graphs
•  Deduce from the shape of a distance-time graph when a
body is:
(i) at rest; (ii) moving with uniform speed; (iii) moving with
non-uniform speed.
•  Deduce from the shape of a speed-time graph when a body
is:
(i) at rest; (ii) moving with uniform speed; (iii) moving with
uniform acceleration; (iv) moving with non-uniform
acceleration.
•  Calculate the area under a speed-time graph to find the
distance travelled at uniform speed or uniform acceleration.
Graphical Analysis of Motion
•  If the car is travelling in only
one direction,
s/m
•  its distance-time graph is also
the displacement-time graph
•  Gradient = velocity
t/s
•  its speed-time graph is also
the velocity-time graph
•  Gradient = acceleration
v/ms-1
t/s
Graphical Analysis of Motion
Distance-time Graph
d/m
Distance of car from
reference point
Reference point
Position of car
Note: Gradient of graph gives the speed of car
Gradient = speed =
Distance
Time
t/s
Graphical Analysis of Motion
Distance-time Graph
Graphical Analysis of Motion
Distance-time Graph
Graphical Analysis of Motion
Distance-time Graph
•  Both objects, A and B, are
moving with constant speed
(straight lines)
distance/m
A
faster
slower
•  Speed of A > Speed of B
(grad of A > grad of B)
B
time/s
Graphical Analysis of Motion
Speed-time Graph
Note: No change in speed, therefore no acceleration.
Graphical Analysis of Motion
Speed-time Graph
Graphical Analysis of Motion
Speed-time Graph
Graphical Analysis of Motion
Speed-time Graph
•  Not all objects move with constant acceleration. Most vehicles
move with accelerations that keep changing.
•  The acceleration or deceleration of the object at any point in time
is still given by the gradient of the graph at that point.
speed/m s-1
stop
stop
time/s
speed-time graph of a car on a straight road where
it has to stop twice because of traffic lights
Graphical Analysis of Motion
Speed-time Graph
Describe the motion of the car
O
Summary
•  If the car is travelling in only
one direction,
s/m
•  its distance-time graph is also
the displacement-time graph
•  Gradient = velocity
t/s
v/ms-1
•  its speed-time graph is also
the velocity-time graph
•  Gradient = acceleration
t/s
Area Under Speed-Time Graph
Graphical Analysis of Motion
Area under a Speed-time Graph
•  The area under a speed-time graph gives the
distance travelled.
Distance = speed x time
= 20 x 5
= 100 m
Graphical Analysis of Motion
Area under a Speed-time Graph
•  The area under a speed-time graph gives the
speed/m s
distance travelled.
-1
Distance = area under graph
V=5
= area of the triangle
= ½ x 10 x 5
= 25 m
time/s
t1= 10
Graphical Analysis of Motion
Distance covered in A = ½ x 10 x 30
= 150m
Distance covered in B = 20 x 30
= 600m
v/ms-1
30
Total distance travelled
B
= 150 + 300 + 150
= 900m
A
C
10
Or ½ (sum of parallel sides) height
= ½ (20 + 40)30
20
30
40
Graphical Analysis of Motion
Average speed = Total Distance
Total Time
= 900/40
v/ms-1
30
= 22.5ms-1
B
A
C
10
20
30
40
Summary
•  If the car is travelling in only one
direction,
s/m
•  its distance-time graph is also the
displacement-time graph
•  Gradient = velocity
•  its speed-time graph is also the
velocity-time graph
•  Gradient = acceleration
•  Area under graph = distance
travelled
t/s
v/ms-1
t/s