Question

With the help of graph, derive the relation v = u + at

Answer 1

Answer:

By the help graph we proved that  v = u + at

Explanation:

$v= u +at$

This equation is called velocity time relation.

To prove this formula draw a velocity time graph in which time is on x-axis and velocity is on y-axis.

Let A be an object moving uniformly with acceleration 'a'.

then ,

Initial velocity at t= 0 is 'u'

and final velocity at t=t is 'v'

From  the graph  we have ,

OA = u (initial velocity)

BC = v (final velocity)

Step 1:

∴ acceleration 'a' = $\frac{change\ in\ velocity}{time \ taken}$

'a' =  $\frac{BE}{AE}$      ⇒ 'a' =  $\frac{BC- EC}{t}$      ( where BE = BC - EC)

'a ' = $\frac{v - u}{t}$ ⇒ at = v -u                  (BC = v and EC = OA = u)

∴v = u + at

Final answer :

Hence , here we proved  v= u +at  with the help of graph.