Question

Let us check the dimensional correctness of the relation $v=u+at$.

Answer 1

Here u represents the initial velocity, v the final velocity, a the uniform acceleration, and t the time.
The dimensional formula of u is $\left[M^{0}L{T}^{-1}\right]$.
The dimensional formula of v is $\left[M^{0}L{T}^{-1}\right]$.
The dimensional formula of at is $\left[M^{0}L{T}^{-2}\right]\left[T\right]=\left[M^{0}L{T}^{-1}\right]$.
Here the dimensions of every term in the given physical relation are the same, hence the given physical relation is dimensionally correct.