Question

An object moves under the action of a force such that distance `(s)` moved by it varies directly as the cube of time taken `(t)`. What is the nature of acceleration of the object? Is it moving under a constant force?

Answer 1

Here, `s prop t^(3)` or `s= kt^(3)`
`:. (ds)/(dt)(=v)= 3 kt^(2)` and `(dv)/(dt)(=a) = 6 kt`
`:. apropt`
i.e., acceleration increases directly with time. As acceleration `a` increases and `F=ma`, therefore, force must also be increasing directly with time. The body is not moving under a costant force.