CBSE Class 9 Answered

We know that the speed of a body = distance travelled / time taken

So let us consider the example of:

1. Speed-time graph when speed remains constant:

If the speed-time graph of a body is a straight line parallel to time axis, then the speed is constant or uniform.

Speed is distance travelled per unit time. i.e speed = distance travelled / time taken.

Thus, we have distance travelled = speed × time.

Consider a point C. Now, in order to find the distance travelled by the body at point C, we draw a perpendicular CB.

Speed at C =CB =OA

Time at C =OC

Thus, distance travelled = Speed × time = OA × OC = Area of rectangle OABC.

Thus, in a speed-time graph, “the area enclosed by the speed-time curve and the time axis gives the distance travelled by the body”.

2. Speed-time graph when speed changes at a uniform rate:

The speed-time graph of a body having uniform changing speed will be a straight line as shown.

Distance can be calculated from the speed-time graph as:

Distance travelled =Area of triangle OPQ

=(1/2) Area of rectangle ORPQ

=(1/2) × OR ×OQ