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

Refer the attachment .. ​

Answer 1

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

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

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