Question

Check the correctness of given equation s = ut + (1/2)at^2

Answer 1

Lets use Dimensional analysis.

$\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2$

LHS:-

$\\ \sf\longmapsto s=\left[M^0LT^0\right]$

RHS

$\\ \sf\longmapsto ut+\dfrac{1}{2}at^2$

$\\ \sf\longmapsto \left[M^0LT^{-1}\right]\left[M^0L^0T^1\right]+\dfrac{1}{2}\left[M^0LT^{-2}\right]\left[M^0L^0T^1\right]^2$

$\\ \sf\longmapsto L+\dfrac{1}{2}\left[LT^{-2}\right]\left[T^2\right]$

$\\ \sf\longmapsto L+\dfrac{1}{2}L$

$\\ \sf\longmapsto \dfrac{2L}{2}$

$\\ \sf\longmapsto [L^1]$

$\\ \sf\longmapsto \left[M^0LT^0\right]$

LHS=RHS

Hence verified