Question

Determine the dimensions of the derivative dx/dt = 3at² b.

Answer 1

The dimensions of the derivative dx/dt = 3at² b are L/T or length per unit time.

Step-by-step explanation:

The dimensions of the derivative dx/dt = 3at² b can be determined by analyzing the dimensions of each term in the equation.

1. The dimension of dx/dt is L/T, which represents length per unit time.
2. Since the equation is dimensionally consistent, all terms on the right side of the equation must have the same dimension.
3. The dimension of 3at² is L (length) and the dimension of b is also L (length).

Therefore, the dimensions of the derivative dx/dt = 3at² b are L/T or length per unit time.