Question

show that:v² =u²+2aS​

Answer 1

Explanation:

S is the displacement covered by any object moving with uniform acceleration.

We can also derive it by following method:-

We know that

v=u+at

Or, t=v−uat=v−ua

Distance travelled = (Average velocity) × (time)

S= v+u2=v+u2×v−uav+u2=v+u2×v−ua

Or, S=v2−u22aS=v2−u22a

→v2−u2=2aS→v2−u2=2aS

Hence, 3rd equation of motion : v2−u2=2aSv2−u2=2aS

V= final velocity

u = initial velocity

a = acceleration

S = Distance covered by object

Answer 2

Explanation:

v² = u² + 2as

We have, v = u + at

written as t = (v-u)/a

Distance = average velocity × Time

(s) = [(v+u)/2] × [(v-u)/a]

s = (v² – u²)/2a

2as = v² – u²

or v² = u² + 2as