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. `4 m//s`
B. `2 m//s`
C. `3 sqrt(2) m//s`
D. `100//3 m//s`

Answer

C

Explanation

`Fvdx = Pdx`
`m xxv^(2) dv = (2+0.2x)dx , v^(2) dv = (1)/(m) (2+0.2m)dx`
`underset(1) overset(v) int v^(2) dv = (7)/(10)[underset(0) overset(10) int 2dx +0.2 underset(0) overset(10) int xdx]`
=`(14)/(10)xx10 +(1.4)/(10)[(100)/(2)] = 14 + 7`
`v^(3) =63 +1 = 64 , v =4m//s`.