Question

If the displacement of a body is proportional to the square of the time elapsed, what type of motion does the body possess?

Answer 1

1. Displacement is defined as a change in the initial and final position of an object.
2. It is a vector quantity and has direction and magnitude.

Here in the given situation, displacement is proportional to the time elapsed.

According to newtons second equation of motion, the displacement is given by

$s=ut+\frac{1}{2}a{t}^2$

Where u is the initial velocity, a is a constant acceleration, time is t, and s is the distance traversed by the body.

$s=ut+\frac{1}{2}a{t}^2$

Let's say the initial velocity is zero,

$s=\frac{1}{2}a{t}^2\Rightarrow s\propto t^2$

If and only if a is constant then displacement will be proportional to time square, this implies that the body will be in uniformly accelerated motion.

Hence, the body will possess uniformly accelerated motion if the displacement of a body is proportional to the square of the time elapsed.