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Question

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in m/s) of the particle is zero, then speed in (m/s) after 5 s is

A
2.5 m/s
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B
5 m/s
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C
10 m/s
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D
3 m/s
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Solution

The correct option is B 5 m/s
Given, mass of particle m=0.2 kg
Power =0.5 W
Work done(w)=F.d
Assume, displacement of particle is d
Final speed of the particle =v
Applying kinematic equation,
v2=u2+2ad
v2=0+2ad
or v2=2ad...(i)

F=ma
Work done w=F.d=ma.d
w=m2(2ad) ....(ii)

From Eq (i) and (ii),
Work done (w)=m2v2 ...(iii)
Power P=dwdt
w0dw=50P dt
w=500.5dt=0.5[t]50

From Eq (iii),
0.2v22=0.5×5
v=25=5 m/s

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