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A machine supplies a particle of mass m with constant power k watts. If the particle is initially at rest, what is the magnitude of the force acting on it at time t?

1. √mk t^(-1/2)
2. √2mk t^(-1/2)
3. (1/2)√mk t^(-1/2)
4. √(mk/2) t^(-1/2)

Correct answer: √(mk/2) t^(-1/2)

Solution

The correct option is derived from the relationship between power, force, and velocity. Since power is the product of force and velocity, and knowing that the particle starts from rest and accelerates under constant power, we can express the force in terms of the power and the time, leading to the result of √(mk/2) t^(-1/2).

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