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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

`4 m s^(-1)`

B

`2 m s^(-1)`

C

`2 sqrt2 m s^(-1)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Area under P-x graph
`=int Pdx = (m (dv)/( dt)) v dx = int_(1)^(v ) mv^(2) dv`
`= [(mv^(3))/(3) ]_(1)^(v) = (10)/( 7 xx 3) (v^(3) - 1)`
From the graph, area `= (1)/(2) (2+4) xx 10=30`
`therefore (10)/(7 xx 3) (v^(3) -1) =30` or `v=4 ms^(-1)`.
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