Motion Graph

Motion graphs can tell you how far a body has travelled, how fast it is moving and all the speed changes there have been.

Distance - time graph ( s-t graph )

Distance of a body from start point is measured. Here are 4 examples of the motion of a car represented by 4 s-t graph

Case 1 : A car is travelling at constant speed
	Case 2 : A car is travelling with increasing velocity
Case 3 : A car is travelling with decreasing velocity
	Case 4 : A car is at rest (stationary)

In a s-t graph, the velocity at any time is given by the slope of tangent to the graph at the instant. If the speed is uniform, the graph inclined straight line.

Speed - time graph ( v-t graph )

v-t graph gives the velocity of a moving object at different time. Here are 4 v-t graph representing the motion of 4 cars:

The acceleration at any time is given by the slope of tangent to the graph at that time

The area enclosed by the graph between a certain time interval represent the displacement of the car travelled during that time interval.

Many students may get confused when they deal with the above graph. We are going to explain it region by region.

• ab : Object increases its velocity from rest. (Acceleration)
• bc : Object decreases its velocity to zero. (Deceleration)
• cd: Object INCREASES its velocity from rest but it travel in REVERSE direction. (ACCELERATION)
• de: Object DECREASES its velocity to zero and it travel in REVERSE direction. (DECELERATION)

Acceleration - time graph ( a-t graph )

The a-t graph gives the acceleration of a moving object at different times.

Here are 3 examples of a-t graph representing the motion of 3 different cars

Case 1 : From this graph, we know that the speed is increasing and the s-t graph should also be increasing with a concave downward shape.
Case 2 : From this graph, we know that the object should either travel in constant speed or at rest.
Case 3 : From this graph, the v-t graph and s-t graph are all increasing with concave downward shape.

The area enclosed by the graph between a certain time interval represents the change in velocity during that time interval.

Oh, the graph with this shape again!!!. This time, it is a a-t graph. Let's see how to interpret it.

• ab : Increasing acceleration (Velocity increases and the rate is faster and faster)
• bc : Decreasing acceleration (Velocity still increases but the rate is slower and slower)
• cd : Increasing deceleration (Velocity decreases and the decreasing rate is faster and faster)
• de : Decreasing deceleration (Velocity decreases but the decreasing rate is slower and slower)

Try the Motion Graph Java. You can plot your own graph!