Question

If the displacement of an object is proportional to the square of time, the object moves with uniform acceleration. Explain.

Answer 1

Dear student,

The Displacement of the object is proportional to the square of the time. ( Assuming s=Displacement and t=time )
Given: s is directly proportional to t^2
s=kt^2 , where k= proportionality constant

Velocity , v =ds/dt
v=d(kt^2) /dt
v=2kt

Now,
acceleration, a=dv/dt
a=d(2kt) / dt
a=2k which is a constant quantity

So, it will be moving with uniform acceleration. The acceleration is not varying with time and is having a constant value and thus, the object is moving with uniform acceleration.


Regards