# CBSE Class 9 Answered

**Show that the area under velocity time graph for uniformly increasing velocity is equal to the distance covered by the body**

Asked by snehanath217 | 09 Apr, 2023, 07:56: PM

Expert Answer

Let the initial velocity of object be u . Let v be the velocity after time duration t.

If change in velocity with respect to time is uniform, then average velocity u

_{avg}in this time duration isDistance S travelled is

S = u

_{avg}× t = (1/2) ( u + v ) t . . . . . . . . . . . . . . . . . . . . (1)Graph below shows the typical variation of velocity that increases uniformly ( constant acceleration )

Line AB shows that velocity varies uniformly from u to v in time t . Time duration is shown as CD on time axis.

If we compare the expression given in eqn.(1) and area under the graph line AB , we see that area under the graph line AB is a trapezium as given by eqn.(1)

Hence , when velocity changes uniformly, then area under the velocity-time graph is the diplacement made in given time

Answered by Thiyagarajan K | 09 Apr, 2023, 10:40: PM

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