Question

Prove the correctness of this equation s=vt + 1/2at ​

Answer 1

The formula is dimensionally correct.

Step-by-step explanation:

Given

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

Required

Prove its correctness

Write out the dimension of each:

`s = M^0LT^0` --- displacement

`ut = M^0LT^(-1) * T` --- velocity * time

`(1)/(2)at^2 = M^0LT^(-2) * T^2` --- acceleration * square of time

The expression becomes:

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

`M^0LT^0 = M^0LT^(-1) * T + M^0LT^(-2) * T^2`

Apply law of indices

`M^0LT^0 = M^0LT^(-1+1) + M^0LT^(-2+2)`

`M^0LT^0 = M^0LT^(0) + M^0LT^(0)`

`M^0LT^0 = M^0LT^(0)`

Both sides of the equation are equal