**Acceleration is related to velocity and time by the following expression: a = vp tq. Find the powers p and q that make this equation dimensionally consistent.**

**Answer:**

The relation for acceleration in terms of velocity and time is

Here, **a** is acceleration, **v** is velocity and **t** is time.

The dimensional formula for acceleration is

The dimensional formula for velocity is

The dimensional formula for time is

**SOLVE:**

The powers and for the dimensional consistency of the given relation are found as follows.

Compare exponents of L on both sides of the above equation.

Compare exponents of T on both sides of the above equation.

Substitute 1 for q in the above equation.

Therefore, the powers p and q for the dimensional consistency of the given relation are

**p = 1** and **q = -1**