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Physics

Write an expression for the distance S covered in time t by a body which is initially at rest and starts moving with a constant acceleration a.

Motion in One Dimension

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Answer

According to equation of motion —

S = ut + $\dfrac{1}{2}$ at²

Where,

S = distance covered

u = initial velocity

a = acceleration

t = time

As, body is at rest, so u = 0

Hence, we get,

$S = (0\times t) + (\dfrac{1}{2} at^2) \\[0.5em] S = 0 + (\dfrac{1}{2} at^2) \\[0.5em] \Rightarrow S = \dfrac{1}{2} at^2 \\[0.5em]$

Hence, we get,

S = $\dfrac{1}{2}$ at²

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