Question

Show the method of dimension to verify weather or not the relation s=ut+½at² is correct

Answer 1

Answer on Question 83857, Physics, Other

Question:

Show the method of dimension to verify whether or not the relation s=ut+½at² is correct.

Answer:

If the relation is dimensionally correct, its left-hand side is equal to the right-hand side. Let's check the dimensions:

$$[s] =[displacement] = L,$$ $$[u] = [speed] = L/T,$$ $$[t] = [time] = T,$$ $$[a] = [acceleration] = L/T^2,$$ $$[t^2] = T^2,$$ $$[ut + 1/2at^2] = (L/T)*L + (L/T^2)*T^2 = L + L = L,$$ $$L = L.$$

As we can see, the relation s=ut+½at² is dimensionally correct.