During a short interval of time the speed v in m/s of an automobile is given by v = at2 + bt3,where the time t is in seconds and a and b are constants. The units of a and b are respectively:
I'm assuming that dimensional analysis is needed for this question. This seems like an odd question since units are in meters per second qubed and meters per second raised to the fourth power.
The Attempt at a Solution
I know the units on the left hand side have to be m/s since it's velocity on the left and so the units on the right hand side must also be m/s. So the units of a and b should be m/s^3 and m/s^4, respectively.
Am I just overthinking this problem or is it really that easy? Is this problem just testing to see if we have any common sense and can do dimensional analysis?