a time dependent fore f=6t acts on a particle of mass 1 kg. if the particle starts from rest the work done by force during the first 1 sec will be ?
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Given in problem that:
the mass of the particle is m = 1 kg,
initially the particle is at rest i.e. u =0
and let the final velocity achieved by particle be v after a time t.
then as we know that, Force = mass x acceleration, we have
=> ∫v0 dv = ∫ 6t dt
=> v = 6[t2/2]10
=> v = 3 ms-1
Thus Work done, W = change in Kinetic Energy = (1/2)* m * v * v
=> W = 0.5 * 1 * 3 * 3
=> W = 4.5 J
the mass of the particle is m = 1 kg,
initially the particle is at rest i.e. u =0
and let the final velocity achieved by particle be v after a time t.
then as we know that, Force = mass x acceleration, we have
=> ∫v0 dv = ∫ 6t dt
=> v = 6[t2/2]10
=> v = 3 ms-1
Thus Work done, W = change in Kinetic Energy = (1/2)* m * v * v
=> W = 0.5 * 1 * 3 * 3
=> W = 4.5 J
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