Question

prove the equation of motion S=ut+at ^2

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Answer 1

Explanation:

Let an object accelerate at a rate a with from initial velocity u to final velocity v in time t covering a distance of s.

We know that in uniformly accelerated motion,

Average velocity = (v + u)/2

V = (v+u)/2. - (1)

Also, velocity = distance * time

V = s/t. - (2)

Equating (1) and (2),

(v+u)/2 = s/t

Using first equation of motion,

v = u + at

s = t (v+u) / 2

s = t (u+u+at) / 2

s = t (2u + at) / 2

s = 2ut/2 + at/2

s = ut + (1/2)at²