Draw a velocity-time graph for a body moving with an initial velocity u and uniform acceleration a.Use this graph to find the distance travelled by the body in time t.

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Solution

In this graph, initial velocity = u
Velocity at time t = v
Let acceleration be ‘a’
Time = t
Then, distance travelled by the body in t s = area between the v-t graph and X-axis
Or distance travelled by the body in t s = area of the trapezium OABD
= $\frac{1}{2} \times (s u m o f p a r a l l e l s i d e s) \times (p e r p e n d i c u l a r d i s t a n c e b e t w e e n t h e m)$
= $\frac{1}{2} \times (u + v) \times (t)$
= $\frac{\frac{u + v}{t}}{2}$

= $\frac{(u + v)}{2 t}$

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Velocity-Time Graphs

Standard IX Physics

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