A stationary particle of mass `m=1.5kg` is acted upon by a variable force. The variation of force with respect to displacement is plotted in figure.
a. Calculate the velocity acquired by the particle after getting displaced through `6m`.
b. What is the maximum speed attained by the particle and at what time is it attained?

Explanation

a. `(x_0-2)/(100)=(4-x_0)/(50)impliesx_0=10/3m`

Total work done, `W=1/2x_0xx100-1/2(6-x_0)50=100J`
`=1/2mv^2=100`
`=1/2xx15/10v^2=100`
`=v=sqrt(2000/15)=20/sqrt3ms^-1`
b. Velocity attained will be maximum at `x=x_0`, become after this work done is negative or force is opposite to velocity.
`W=1/2xx10/3xx100=500/3J`
`implies1/2mv^2=500/3`
`implies1/2xx15/10v^2=500/3`
`impliesv=sqrt((5000xx2)/(45))=(10sqrt20)/(3)ms^-1=20/3sqrt5ms^-1`