venkat
Last Activity: 6 Years ago
Given,
Mass of the particle = m
Velocity varies linearly with distance travelled as
v=bx1/2
Force acting on the body,
F=ma
F=m*dv/dt
F=m*(dv/dx)*(dx/dt) [Multiplying and dividing with ‘dx’]
F=mv*(dv/dx) [
dx/dt=v]
F=mv*(d(bx1/2)/dx)
F=m(bx1/2)(bx-1/2/2)
F=mb2/2
Distance moved by by the body in first ‘t’ seconds is given by
v=dx/dt
dt=dx/v
Integrating on both sides, we get
dt=
dx/v
t=(1/b)
dx/(x
1/2)
t=(2/b)*x1/2
t=(2x1/2)/b
i.e., distance travelled by the body in first t seconds s=b2t2/4
Work done by the force on the body in first t seconds is given by
W=Fs
W={mb2/2}*{b2t2/4}
Work done W=mb
4t
2/8
