Dimensions of Velocity Equation

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SUMMARY

The dimensions of the constants A and B in the velocity equation v = At³ - Bt⁴ are determined to be A = m/s⁴ and B = m/s⁵, respectively. This conclusion is reached by analyzing the equation in terms of dimensional analysis, where velocity is expressed in meters per second (m/s). By substituting time (t) in seconds (s) into the equation, the dimensions of A and B are derived through algebraic manipulation, ensuring that the units remain consistent throughout 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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