Question

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

Answer 1

Answer:

The formula is dimensionally correct.

Explanation:

Given

$s = ut + \frac{1}{2}at^2$

Required

Prove its correctness

Write out the dimension of each:

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

$ut = M^0LT^{-1} * T$ --- velocity * time

$\frac{1}{2}at^2 = M^0LT^{-2} * T^2$ --- acceleration * square of time

The expression becomes:

$s = ut + \frac{1}{2}at^2$

$M^0LT^0 = M^0LT^{-1} * T + M^0LT^{-2} * T^2$

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