Draw velocity-time graph for a body moving with uniform velocity. Hence show that the area under the velocity-time graph gives the distance travelled by the body in a given time interval.

Explanation

In uniform-motion, velocity of-a-body remains.constant.with respect to time. Therefore, velocity time graph will be a straight line parallel to time axis as shown in the figure.
Conside two points P and Q on the graph correspoinding to times `t _(0)` and t respectively.
Area of rectangle `PQRS = PS xx PQ = v xx (t - t _(0)) `
But `v =(x - x _(0))/( t - t _(0))`
Therefore, area under v - t graph ` = (x - x _(0))/( t - t _(0)) xx (t - t _()) = x - x _(0)`
Since ` x-x_(0)` is the displacement of the body , therefore, area under velocity time graph is equal to displacement of the body during given time interval.