Question

A student has derived the following nondimensionally homogeneous equation:a=x/t^2 − vt + F/m where v is a velocity's magnitude, a is an acceleration's magnitude, t is a time, m is a mass, F is a force's magnitude, and x is a distance (or length). Which terms are dimensionally homogeneous? Check all that apply. I know the answers are1 2 and 4 but don't know why. explain so I can understand.
1) x/t^2
2) a
3) F/m
4) vt

Answer 1

answers are1 2 and 3.

Answer 2

1. is meters/second^2

2. is meters / second^2

3. is newtons / kilograms but we all know from Newton's second law that Newtons = kilograms* meters/second^2 so 3. is also meters/second^2

4. (meters / second) * seconds = meters. TILT !

Answer 3

Do your other problem the same way.