Assume the equation x 5 at3 1 bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimen- sions of the constants a and b. (b) determine the dimen- sions of the derivative dx/dt 5 3at2 1 b.

(a) A = m/s^3, B = m/s.

(b) dx/dt = m/s.

Explanation:

(a)

Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.

(b)

This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.

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