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