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
Answers
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