What Are the Units and Exponents in Basic Physics Equations?

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Understanding units and exponents in physics equations is crucial for grasping the subject. For the equation v = at^2 + bt^3, the units of a must be m/s^3 and b must be m/s^4 to ensure dimensional consistency. In the second equation A = B^n * C^m, the dimensions imply that n should equal 1 and m should equal 1 to maintain dimensional balance. It's important to remember that the units on both sides of an equation must match, and while you can multiply or divide different units, you can only add or subtract like units. Mastering these concepts is essential for solving basic physics problems effectively.
Catalyst333
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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:
 
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You need to show your work before we can help-- forum rules. What do you know about the dimensions of an equation?
 
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 :(
 
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
 
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