#### If the displacement of an object is proportional to square of time, then the object moves with(a) uniform velocity(b) uniform acceleration(c) increasing acceleration(d) decreasing acceleration

Ans. B

Sol.

If the object moves with uniform velocity the displacement increases linearly with time. That means displacement will be proportional to time.

In case of uniform acceleration, we can use equation of motion.

$v = u + at$

$s = ut + \frac{1}{2}$

$v^{2}=u^2 + 2as$

If we observe second equation of motion carefully for zero initial velocity, We will observe that displacement is proportional to square of time.

$s = \frac{1}{2}at^2$

In case of variable acceleration, whether it is increasing or decreasing, the displacement will not be proportional to square of time.

Hence the correct option is B.