To be dimensionally consistent, velocity [L/T], acceleration [L/T²] and time [T] must be related as follows. A) velocity = acceleration × time B) velocity = acceleration × time² C) velocity = acceleration² × time² D) velocity = acceleration² × time

Question

Quizplus · Accepted Answer

Velocity is defined as the rate of change of displacement with respect to time, which can be expressed as v = Δx/Δt. Taking the derivative of velocity with respect to time gives us acceleration, a = dv/dt. Rearranging these equations, we get v = a * t, which shows that velocity is equal to acceleration multiplied by time. This makes option A the correct choice. Option B and D are incorrect because they include additional terms that do not cancel out dimensionally, while option C is incorrect because it multiplies the acceleration term by an incorrect power of time.

To Be Dimensionally Consistent, Velocity [L/T], Acceleration [L/T2] and Time

To Be Dimensionally Consistent, Velocity [L/T], Acceleration [L/T²] and Time