Powers of p and q from a=v^p*t^q

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The equation a = v^p * t^q requires specific values for p and q to maintain dimensional consistency. Given that acceleration (a) has units of m/s², velocity (v) has units of m/s, and time (t) has units of s, the only valid solution is p = 1 and q = -1. This ensures that the dimensions on both sides of the equation match, confirming the relationship between these physical quantities.

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How do I go about solving for the powers of p and q to make the equation dimensionally consistent?

Any help or advice would be much appreciated! :smile:
 
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I'm assuming v is velocity, t is time and a is acceleration?

Acceleration has units of m/s2, while velocity has units of m/s. So the only valid values of p and q would have to be p = 1 and q = -1.
 
dipole said:
I'm assuming v is velocity, t is time and a is acceleration?

Acceleration has units of m/s2, while velocity has units of m/s. So the only valid values of p and q would have to be p = 1 and q = -1.

Yes, I failed to mention that. Thank you for your help. :smile:
 

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