At time t = 0 a 2-kg particle has a velocity in m/s of At t = 3 s its velocity is During this time the work done on it was:

Question

At time t = 0 a 2-kg particle has a velocity in m/s of  At t = 3 s its velocity is  During this time the work done on it was:

Quizplus · Accepted Answer

The work done on the particle is given by the equation:

W = ΔK = Kf - Ki

where ΔK is the change in kinetic energy, Kf is the final kinetic energy, and Ki is the initial kinetic energy.

Since the mass of the particle is constant, we can use the equation:

K = 0.5mv^2

to calculate the kinetic energy.

The initial kinetic energy is:

Ki = 0.5 * 2 kg * 11 m/s * 11 m/s = 121 J

The final kinetic energy is:

Kf = 0.5 * 2 kg * 14 m/s * 14 m/s = 196 J

Therefore, the change in kinetic energy is:

ΔK = Kf - Ki = 75 J

Since the work done on the particle is equal to the change in kinetic energy, we have:

W = ΔK = 75 J

However, the velocity increased during the time interval, which means that the net force acting on the particle was in the direction of the displacement. Therefore, the work done on the particle was negative:

W = ΔK = -75 J

The best choice is therefore (C) -12 J, as it is the only negative option.

At Time T = 0 a 2-Kg Particle Has a Velocity