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A particle starts moving from rest the o...

A particle starts moving from rest the origin `&` moves along positive `x-` direction . Its rate of change of kinetic energy with time shown on `y-` axis veries with time `t` as shown in the graph. If position, velocity , acceleration `&` kinetic energy of the particle at any time `t` are `x,v,a,& k` respectively then which of the option `(s)` may be correct ?

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`(dk)/(dt)prop t`
`rArr k prop t^(2) .....(i)`
`rArr v prop t ...(ii)`
`rArr v vs t:st. ` line
`rArr x propt^(2) ....(iii)`
`rArr x vs t :` parabola
`(i) & (iii)`
`rArr k prop x :` st. line
`(ii)rArra=` constant
`(ii) & (iii) rArr v^(2) prop x .....(v) v^(2)vs x: st. `line
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