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Question

A particle of mass 12 kg is acted upon by a force f =(1002x2) when f is in newton and x is in metre. Calculate the wrok done by this force in moving the particle x=0 to x=10m. What will be the speed at x=10m if it starts from rest.

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Solution

Given ForceF=1002x2
And we know work done ΔW=Fdx where dx=displacement.
Now integrating the above equation from limits x=0 to x=10,we get,
W=100(1002x2)dx=|100x|100|23(x3|100=3000+20003=333.33J negative sign implies work is done by the system.
Also we know W=Fs where s=displacement=vt where v=velocity and t= time.
And Force F=ma=mvt given initial velocity u=0 m/s.
So work done W=mv2
333.3312=v
v=5.27m/s

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