If the displacement of an object is proportional to the sq.of time then the object is moving with uniform acceleration.Explain why. Please explain it in the simplest form

Dear student,
The Displacement of the object is proportional to the square of the time.Assuming s=Displacement and t=time.
s is directly proportional to t^2
s=kt^2 where k= proportionality constant
Velocity , v =ds/dt
v=dkt^2/dt
v=2kt
Now, acceleration, a=dv/dt
a=d2kt/dt
a=2k which is a constant quantity
So, it will be a motion 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