  Question

A constant force of $$2.50\ N$$ accelerates a stationary particle of mass $$15\ g$$ through a displacement of $$2.50\ m$$. Find the work done and the average power delivered.

Solution

Given that Force $$F = 2.5\ N$$. Mass of the particle $$m = 15\ g =0.015\ kg$$ Displacement covered by the particles $$s = 2.5\ m$$. Now, For Work, Work Done = Force × Displacement  $$W=2.5\times 2.5$$  $$W=6.25\,J$$ Hence, the Work done by the Particles is $$6.25\ J$$. Now, For Power, Work Done = $$6.25\ J$$. Initial Velocity $$u = 0$$ Using Newton's second law of Motion,   $$F=ma$$  $$a=\dfrac{m}{F}$$  $$a=\dfrac{2.5}{0.015}$$  $$a=166.67\,m/{{s}^{2}}$$  Now, the time taken for the displacement is:$$s=ut+\dfrac12at^2$$ $$2.5=0+\dfrac12\times\dfrac{500}{3}\times t^2$$$$t=\sqrt{\dfrac{5\times3}{500}}=0.1\sqrt3$$ Now, Power = Work/Time.   $$P=\dfrac{W}{t}$$  $$P=\dfrac{6.25}{0.1\sqrt{3}}$$  $$P=36.08\,W$$ Hence, the work done is $$6.25 J$$ and power is $$36.08 W$$Physics

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