Answer to Question #78219 in Physics for Dennis Kopman

Question

The velocity v of a moving object is related to the displacement x, and the acceleration a, by relation V^n = 2ax, use dimensional analysis to find the value of n.

Answer 1

Let us apply the dimensional analysis to relation
v^n = 2ax
We get
[L/T]^n=[L/T^2 ]×[L]
[L/T]^n=[L^2/T^2 ]=[L/T]^2
So
n=2