Question

The distance x traveled by a body in time t which starts from the position x0 with initial velocity u0 and has uniform acceleration a, is given by x = x0 + u0t + Check the dimensionally consistency of this equation.

Answer 1

Answer:

Example of checking for dimensional consistency

Consider one of the equations of constant acceleration,

s = ut + 1/2 at2. (1)

The equation contains three terms: s, ut and 1/2at2. All three terms must have the same dimensions.

s: displacement = a unit of length, L

ut: velocity x time = LT-1 x T = L

1/2at2 = acceleration x time = LT-2 x T2 = L

All three terms have units of length and hence this equation is dimensionally valid. Of course this does not tell us if the equation is physically correct, nor does it tell us whether the constant 1/2 is correct or not.