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Standard XII

Physics

Relation between Work Done and PE

Displacement ...

Question

Displacement of a particle of mass 2 kg varies with time as: $s = (2 t^{2} - 2 t + 10) m .$ Find total work done on the particle in a time interval from t=0 to t=2 s.

16 J

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32 J

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48 J

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96 J

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Solution

The correct option is B 32 J
Acceleration of the particle is given by $a = \frac{d^{2} s}{d t^{2}}$
$= 4 m / s^{2}$
Thus force acting on the particle= $m a = F = 8 k g m / s^{2}$
Work done on the particle= $\int_{0}^{t} F d s$
$= F Δ s$
At $t = 0, s = 10 m$
At $t = 2, s = 14 m$
Thus work done= $32 J$

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Displacement of a particle of mass 2 kg varies with time as: s=(2t2−2t+10)m. Find total work done on the particle in a time interval from t=0 to t=2 s.

The correct option is B 32 JAcceleration of the particle is given by a=d2sdt2=4m/s2Thus force acting on the particle=ma=F=8kgm/s2Work done on the particle=∫t0Fds=FΔsAt t=0,s=10mAt t=2,s=14m Thus work done=32J

Displacement of a particle of mass 2 kg varies with time as: $s = (2 t^{2} - 2 t + 10) m .$ Find total work done on the particle in a time interval from t=0 to t=2 s.