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, the speed (in m/s) after 5 s is:

Answer 1

In this question, we have been asked to calculate the velocity of the particle after 5 seconds of time. It is given that initial velocity is zero. The mass and power required is also given. Now, we know that total work done on the particle will be equal to the change in kinetic. Therefore, we will be using this relation to calculate the velocity of a given particle.

Complete answer:
We know that the mass of a particle is 0.2 kg. The power required to move the particle is 0.5 W. Now, we know that the work done is equal to change in the kinetic energy.
Therefore, we can say
$W=\Delta K.E$ ……….. (1)
We also know that, work done is given by
$W=P\times t$
The power is given as 0.5 W and time t = 5 seconds
Therefore,
$W=0.5\times 5$ ……. (2)
From (1) and (2)
We get,
$0.5\times 5=\Delta K.E=\dfrac{1}{2}m{{v}^{2}}$
Therefore,
$2.5=\dfrac{1}{2}m{{v}^{2}}$
On solving,
We get,
$v=5m/s$
Therefore, the velocity of the particle after 5 seconds is 5 m/s.

Note:
When a work is done on an object due to some external force, the energy of the particle is transferred. The rate at which this energy is transferred is called Power. That means a more powerful device will transfer more energy. When an object is moved due to the external force, the work is done on that object. Work done is given as the product of force applied and the distance the object is moved with the same force.