Question

prove the third equation of motion-
$v ^{2} = u^{2} + 2as$
​

Answer 1

Answer:

Explanation:

Considering a velocity time graph for a body having some non zero initial velocity at time t = 0.

where -

u: velocity at time t1  

v: velocity at time t2  

a: uniform acceleration of the body along the straight line

Thus, the displacement covered during the time interval t2 - t1 = Area ABt1t2

S = Area of triangle ABA’ + Area of rectangle AA’t2t1  = Area of trapezium  

S = 1/2 x Sum of parallel sides x Perpendicular distance

S = 1/2 (v+u)t

First equation of motion, v = u + at; or t = v-u/a

Thus,

1/2(v+u)(v-u)/a

or v²-u² = 2as, the required equation of motion