Question

show that S=vit+1/2at2 is dimensionally correct
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Answer 1

Explanation:

check the attachment

Answer 2

Given: $s=ut+\frac{1}{2}at^2$

where S is the distance, t is time, u is initial velocity and a is acceleration.

Using MLT dimension rule.

$s=ut+\frac{1}{2}at^2$

$L=[LT^{-1}][T]+\frac{1}{2}[LT^{-2}][T]^2$

$L=[L]+\frac{1}{2}[L]$

In addition, we add a similar identity and the resultant is similar to added number.

Hence RHS side of the expression is in Length. Similar to the LHS.

Hence proved

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