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.)
What are the dimensions of B?

I am assuming that the equation you meant to write is this:

v = At^3 - Bt^4

Note that we use the "^" symbol to mean "to the power of."

I'll help you with figuring the dimension of A, then you can figure out B, OK? Since v has the dimension meters per second, that means that the quanity At^3 is also in meters/sec. The quantity t is time, in seconds. Hence you have:

m/s = A s^3, which you can rearrange:
A = (m/s)/(s^3) = m/(s^4)
Or meters per second to the 4th power.

Now, can you solve for the dimension of B?