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A particle A of mass 10//7kg is moving i...

A particle A of mass `10//7kg` is moving in the positive direction of x-axis. At initial position `x=0`, its velocity is `1ms^-1`, then its velocity at `x=10m` is (use the graph given)

A

(a) `4ms^-1`

B

(b) `2ms^-1`

C

(c) `3sqrt2ms^-1`

D

(d) `100/3ms^-1`

Text Solution

Verified by Experts

The correct Answer is:
A
Area under `P-x` graph
`=int pdx=(m(dv)/(dt))vdx=underset1oversetvintmv^2dV`
`=[(mv^3)/(3)]_1^v=(10)/(7xx3)(v^3-1)`
From the graph, `area=1/2(2+4)xx10=30`
or `(10)/(7xx3)(v^3-1)=30`
or `v=4ms^-1`
Alternative method:
From graph
`P=0.2x+2`
`mv(dv)/(dx)v=0.2x+2`
`mv^2dv=(0.2x+2)dx`
Now integrating both sides, we get
`underset1oversetvintmv^2dv=underset0overset10int(0.2x+2)dx`
`v=4ms^-1`
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