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.
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
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