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)

Options

A. (a) `4ms^-1`
B. (b) `2ms^-1`
C. (c) `3sqrt2ms^-1`
D. (d) `100/3ms^-1`

Answer

A

Explanation

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`