Question

Using dimensional analysis prove that v=u+at is dimensionally correct​

Answer 1

Explanation:

Here, the equation is-

v= u +at

The dimensions of individual terms are as following-

[V] = [L]/[T] =[LT⁻¹]

[U] = [L]/[T] =[LT⁻¹]

[AT] = [A] [T] = [LT⁻². T] = [LT⁻¹].

Here, we see that, the dimensions of all the individual terms are same, so Principle of Homogeneity is satisfied.

Hence, the equation is dimensionally correct.

Answer 2

Answer:

See :

Explanation:

V = velocity or distance/time

dimensionaly = [L][T]^-1

u =  [L][T]^-1

a = [L][T]^-2

t = [T]

so, L.H.S = v

               = [L][T]^-1

R.H.S = u + at

          =  [L][T]^-1 +  [L][T]^-2 *  [T]

          =  [L][T]^-1  +  [L][T]^-1

          = c   [L][T]^-1

          =   [L][T]^-1

so, LHS =RHS