A stationary particle of mass 15 g is accelerated by a constant force of 2.50 N over a displacement of 2.50 m . Determine the work done and the average power delivered.

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Quantrex Academy · Accepted Answer

Correct answer: B. 6.25 J , 36.1 W

Work done by the constant force is given by:

W = Fs = 2.50 \times 2.50 = 6.25 \text{ J}

Acceleration of the particle is:

a = \dfrac{F}{m} = \dfrac{2.50}{15 \times 10^{-3}} = \dfrac{500}{3} \text{ m/s}^2

Using the equation of motion

v^2 = u^2 + 2as

with

u = 0

:

v^2 = 0 + 2 \times \dfrac{500}{3} \times 2.50 = \dfrac{2500}{3}

v = \dfrac{50}{\sqrt{3}} \text{ m/s}

For constant acceleration, the average velocity is:

v_{avg} = \dfrac{u+v}{2} = \dfrac{25}{\sqrt{3}} \text{ m/s}

Average power delivered is:

P_{avg} = F \times v_{avg} = 2.50 \times \dfrac{25}{\sqrt{3}} = \dfrac{62.5}{\sqrt{3}} \approx 36.1 \text{ W}

A stationary particle of mass 15 g is accelerated by a constant...

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