Dimensions of Velocity Equation

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The speed of an object is defined by the equation v = At^3 - Bt^4, where A and B are constants with specific dimensions. To determine the dimensions of A, it is established that A must equal m/s^4, while B equals m/s^5. This is derived from the requirement that the overall equation must yield a velocity dimension of m/s. By analyzing the terms, it becomes clear that the time components (t^3 and t^4) influence the dimensions of A and B accordingly. Understanding these relationships clarifies the dimensional analysis of the equation.
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Homework Statement



The speed, v, of an object is given by the equation v = At3 - Bt4 where t refers to time. What are the dimensions of A? (Express your answers using only m for distance and s for time.)

Homework Equations





The Attempt at a Solution



I know the answer. A is m/s4 and B is m/s5
I just do not know why that is. I want to have an understanding of why, rather then just knowing what to do.
Thank you in advance.
 
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Okay you do know that velocity is m/s right?

so looking at the first term a * t * t *t the t's provide s^3 so then the A must be m/s^4 when multiplied together three of the s's are canceled out leaving A t^3 to be m/s

You can do this symbolically like this:

(m/s) = A (s^3) and dividing both sides by s^3 we get A = (m/s^4)

similarly for (m/s) = B (s^4) hence B = (m/s^5)
 
Oh i see! They just want m/s! Completely understand now. Thank you
 

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