Graphical Representation of Motion

Distance-Time Graphs

The change in the position of an object with time can be represented on the  distance-time graph adopting convenient scale of choice. In this graph fig2 ,time is taken along the x-axis and distance is taken along the y-axis. Distance-time graphs can be employed under various conditions where objects move with uniform  speed , non-uniform speed, remain at rest etc.

We know that when an object travels equal distance in equal interval of time, it moves with uniform speed. This shows that the distance travelled by the objects is directly proportional to the time taken. Thus , for uniform speed, a graph of di

stance travelled against time is a straight line , as shown in fig2. The portion OB of the graph shows that the distance is increasing at a uniform rate.

We can use the distance-time graph to determine the speed of an object. To do so, consider a small part AB of the distance –time graph shown in fig 2. Draw a line parallel to the x-axis from point A and another line parallel to the y –axis from the point B. These two lines meets each other at point C to form a triangle ABC.Now,on the graph,AC denotes the time interval(t₂-t₁) while BC corresponds to the distance(s2-s1). We can see from the graph that as the object moves from the point A to B, it cover a distance(s2-s1) in the (t2-t1). The speed,v of the object, therefore  can represented as

We can also plot the distance-time graph for accelerated motion.

The nature of this graph shows non-linear variation of the distance travelled by the car with time.

Velocity-Time Graphs

The  variation in velocity with  time for an object moving  can be represented by a velocity-time graph.

When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a steadily increasing velocity, or a steadily decreasing velocity, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph.