Question

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.)

Answer 1

A = LT⁻³

B = LT⁻¹

Step-by-step explanation:

x = At³ +Bt

According to dimensional formula law , Physical quantity having similar dimension can only be added or subtracted.

so dimension of x = dimension of At³

L = AT³

A = LT⁻³

So , dimension of A = LT⁻³

again,

dimension of x = dimension of Bt

L= BT

B = LT⁻¹