What are the dimensions of A and B?

Question

This is exactly how the problem reads:

The speed, v, of an object is given by the equation: v=(At^3) - (Bt), where t refers to time. What are the dimensions of A and B?

i am sooo lost, and would really appreciate help.

Answer 1

Since v is m/s (distance over time), then the two terms have to have the same units.

At³ = m/s

A = m/s (sec^-3)

A is in m/s⁴ or distance over time raised to the fourth

Bt = m/s

B = m/s² or distance over time squared.

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Answer 2

Each of the terms must have units of velocity, m/s.

So consider the first term: A(sec^3) = m/s

Solve for A and you get m/s^4. That is what the units of A must be to give you units of velocity for that term.

Now consider the second term  B(sec)=m/s  

So B must have units m/s^2.