Question

Consider the physical quantities s, v, a, and t with dimensions [s]=L, [v]=LT−1, [a]=LT−2, and [t]=T. Determine whether each of the following equations is dimensionally consistent.

(a) v2=2as;
(b) s=vt2+0.5at2;
(c) v=s/t;
(d) a=v/t.

Answer 1

The provided equations are dimensionally consistent. Each equation has the same dimensions on both sides of the equation. Therefore, the correct answer is (a) v2=2as.

Step-by-step explanation:

The first equation v2 = 2as is dimensionally consistent because both sides of the equation have the same dimensions. The left side is [(LT-1)2] = (L2T-2) and the right side is [2(L)(L)] = (L2T-2).

The second equation s = vt2 + 0.5at2 is dimensionally consistent because both sides of the equation have the same dimensions. The left side is [(L)] and the right side is [(LT-1)(T2) + (LT-2)(T2)] = (L).

The third equation v = s/t is dimensionally consistent because both sides of the equation have the same dimensions. The left side is [(LT-1)] and the right side is [(L)/(T)] = (LT-1).

The fourth equation a = v/t is dimensionally consistent because both sides of the equation have the same dimensions. The left side is [(LT-2)] and the right side is [(LT-1)/(T)] = (LT-2).