What Are the Units and Exponents in Basic Physics Equations?

[Catalyst333]

I am very embarrassed to ask these questions because compared to other questions on these boards, these two seem very basic. Nonetheless, I have never taking physics and I am having a hard time grasping its concepts. So here are two simple questions that maybe someone could answer and explain for me. Thanks!

1st Q: During a short interval of time the speed v in m/s of an automobile is given by v = at^2 + bt^3, where the time t is in seconds. The units of a and b should be?

2nd Q: Suppose A = B^n*C^m, where A has dimensions LT, B has dimensions L^2T^–1, and C has dimensions LT^2. Then the exponents n and m have the values:

 

[cristo]

You need to show your work before we can help-- forum rules. What do you know about the dimensions of an equation?

 

[Catalyst333]

To be honest, I have no idea where to start with these two questions. I was hoping someone could get me started with either one. The only thing I know about dimensions is that acceleration is Length/Time^2 and speed is Length/time. My teacher zipped through this part and the book does not seem to talk about it. In other words, i don't know much about dimensions :(

 

[mgb_phys]

The units on both sides of an equation must be the same.
You can multiply/divide different units but you can only add/subtract the same units ( a bit like canceling fractions).

so, area (m^2) = length(m) * width(m)
or, distance(m) = speed(m/s)*time(s) + 1/2 acceleration(m/s^2)*time(s)^2