Acceleration is related to velocity and time by the following expression: a = vp tq

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
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Here, a is acceleration, v is velocity and t is time.
The dimensional formula for acceleration is
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The dimensional formula for velocity is
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The dimensional formula for time is
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SOLVE:
The powers and for the dimensional consistency of the given relation are found as follows.
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Compare exponents of L on both sides of the above equation.
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Compare exponents of T on both sides of the above equation.
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Substitute 1 for q in the above equation.
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Therefore, the powers p and q for the dimensional consistency of the given relation are
p = 1 and q = -1