Dimensions of Velocity Equation

[OUstudent]

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.

 

[jedishrfu]

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)

 

[OUstudent]

Oh i see! They just want m/s! Completely understand now. Thank you