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/sGiven, 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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