Question

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

Answer 1

Lets use Dimensional analysis.

`\\ \sf\longmapsto s=ut+(1)/(2)at^2`

LHS:-

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

RHS

`\\ \sf\longmapsto ut+(1)/(2)at^2`

`\\ \sf\longmapsto \left[M^0LT^(-1)\right]\left[M^0L^0T^1\right]+(1)/(2)\left[M^0LT^(-2)\right]\left[M^0L^0T^1\right]^2`

`\\ \sf\longmapsto L+(1)/(2)\left[LT^(-2)\right]\left[T^2\right]`

`\\ \sf\longmapsto L+(1)/(2)L`

`\\ \sf\longmapsto (2L)/(2)`

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

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

LHS=RHS

Hence verified