Question

a body moves in such a way that displacement is directly proportional to the cube of the time elapsed, then the motion is
1)uniform motion
2)uniform acceleration
3)non uniform acceleration
4)any of the above is possible

Answer 1

According to the question,  

x ∝ t³

differentiating distance we get velocity

dx/dt =3t²

 v ∝ t²

Differentiating velocity we get acceleration

dv/dt = 2t

a ∝ t

Here, acceleration depends on time

Therefore the motion will be non-uniform acceleration, as the acceleration will keep changing as time will change.

Answer 2

Given :

A body moves in such a way that displacement is directly proportional to the cube of the time elapsed,

To Find :  the motion is

1)uniform motion

2)uniform acceleration

3)non uniform acceleration

4)any of the above is possible

Solution:

v = ds/dt

a = dv/dt = d²s/dt²

a = acceleration

v = velocity

s = displacement

t = time

s ∝ t³

=> s = kt³     k is a constnt

v = ds/dt  = 3kt²

a = dv/dt = d²s/dt²  = 6kt

Hence a ∝ t

a is proportional to t

Hence a is not constant , it varies with time

so non uniform acceleration  is the correct answer

option 2) is correct answer

uniform motion : Velocity is constant

uniform acceleration : Velocity increased at constant rate.  Acceleration is constant

Learn More:

A ball starts moving eastward with speed 35 m/s. An acceleration of ...

brainly.in/question/8968403

What is the acceleration of a rock thrown straight upward on the way ...

brainly.in/question/18127144