Question

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.

Answer 1

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
= $\frac{1}{2}\times \left(sumofparallelsides\right)\times \left(perpendiculardistancebetweenthem\right)$
=$\frac{1}{2}\times (u+v)\times \left(t\right)$
=$\frac{\frac{u+v}{t}}{2}$

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