Question

Show that v=u +at by using v-t graph

Answer 1

Explanation:

The body has an initial velocity u at a point A and then its velocity changes at a uniform rate from A to B in time t. In other words, there is a uniform acceleration a from A to B, and after time t its final velocity becomes v which is equal to BC in the graph. The time t is represented by OC.

To complete the figure, we draw the perpendicular CB from point C, and draw AD parallel to OC. BE is the perpendicular from point B to OE.

Now, Initial velocity of the body, u=OA ...(1)

And, Final velocity of the body, v=BC ...(2)

But from the graph BC=BD+DC

Therefore, v=BD+DC ...(3)

Again DC=OA

So, v=BD+OA

Now, from equation (1), OA=u

So, v=BD+u .....(4).

We should find out the value of BD now. We know the slope of a velocity-time graph is equal to the acceleration, a.

Thus, Acceleration, a= slope of line AB

or a=BD/AD

But AD=OC=t, so putting t in place of AD in the above relation, we get:

a= BD/t

or BD=at

Now, putting this value of BD in equation(4), we get:

v=u+at