Question

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

Answer 1

increasing acceleration

Answer 2

Answer:

option B

Explanation:

Given that, displacement of an object is promotional to the square of time i.e. s ∝ t².

Let us assume that the initial velocity of the object is 'u', final velocity is 'v', it's acceleration is 'a', displacement/distance covered by the object is 's' in time 't'.

Using the First Equation Of Motion,

v = u + at

If object starts from rest then it's initial velocity i.e. u becomes 0 m/s.

→ v = 0 + at

→ v = at

Here, a is constant. So,

→ v ∝ t

But in question, we are talking about displacement which is directly proportional to square of time.

So,

Using the Second Equation Of Motion,

s = ut + 1/2 at²

If object starts from rest then it's initial velocity i.e. u becomes 0 m/s.

→ s = (0)t + 1/2 at²

→ s = 0 + 1/2 at²

→ s = 1/2 at²

Here, 1/2 and a are constant. So,

→ s ∝ t²

Therefore, object is moving with constant/uniform acceleration.

Option b) Uniform acceleration