Question

(a) Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.)[A] = ????[B] = ????(b) Determine the dimensions of the derivative dx/dt = 3At2 + B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.)[dx/dt] = ?????

Answer 1

Answer:

A = [L*T^-3]

B = [L*T^1]

Explanation:

The equation

x = A*t^3 + B*t

has multiple terms that when added together result in x. We know x has dimension of length, so all the terms must have dimensions of length too.

A*t^3 = [L]

A*[T^3] = [L]

A = [L/T^3]

A = [L*T^-3]

And

B*t = [L]

B*[T] = [L]

B = [L/T]

B = [L*T^-1]