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,

•  its distance-time graph is also the displacement-time graph

•  Gradient = velocity

•  its speed-time graph is also the velocity-time graph

•  Gradient = acceleration

s/m

t/s v/ms-1

t/s

Graphical Analysis of Motion Distance-time Graph d/m

t/s Reference point

Distance of car from reference point

Position of car

Note: Gradient of graph gives the speed of car

Gradient = speed = Distance Time

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)

•  Speed of A > Speed of B (grad of A > grad of B)

distance/m

time/s

faster

slower

A

B

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-time graph of a car on a straight road where it has to stop twice because of traffic lights

time/s

speed/m s-1

stop stop

Graphical Analysis of Motion Speed-time Graph Describe the motion of the car

O

Summary •  If the car is travelling in only

one direction,

•  its distance-time graph is also the displacement-time graph

•  Gradient = velocity

•  its speed-time graph is also the velocity-time graph

•  Gradient = acceleration

s/m

t/s v/ms-1

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

distance travelled.

Distance = area under graph

= area of the triangle

= ½ x 10 x 5

= 25 m

speed/m s-1

time/s

V = 5

t1= 10

Graphical Analysis of Motion

v/ms-1

30

10 3020 40

A

B

C

Distance covered in A = ½ x 10 x 30 = 150m

Distance covered in B = 20 x 30 = 600m

Total distance travelled

= 150 + 300 + 150

= 900m

Or ½ (sum of parallel sides) height

= ½ (20 + 40)30

Graphical Analysis of Motion

Average speed = Total Distance Total Time

= 900/40

= 22.5ms-1

v/ms-1

30

10 3020 40

A

B

C

Summary •  If the car is travelling in only one

direction,

•  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

s/m

t/s v/ms-1

t/s