Question

a nonzero net force acts on a particle and does work. which one of the following statements is true?
the kinetic energy and the speed of the particle change, but the velocity of the particle does not change.
the kinetic energy of the particle changes, but the velocity of the particle does not change.
the kinetic energy of the particle changes, but the speed of the particle does not change.
the kinetic energy, speed, and velocity of the particle change.
the kinetic energy of the particle does not change, but the speed of the particle does change.

Explanation:

Step1: Recall work - energy theorem

The work - energy theorem states that the net work done on an object is equal to the change in its kinetic energy, $W_{net}=\Delta K=\frac{1}{2}mv^{2}_{f}-\frac{1}{2}mv^{2}_{i}$. If a non - zero net force does work on a particle, its kinetic energy $K = \frac{1}{2}mv^{2}$ changes.

Step2: Analyze the relationship between kinetic energy, speed and velocity

Since $K=\frac{1}{2}mv^{2}$, when $K$ changes, the speed $v$ (the magnitude of velocity) must change. And if the speed changes, the velocity (which is a vector with both magnitude and direction) also changes because the magnitude of the velocity vector is the speed.

Answer:

The kinetic energy, speed, and velocity of the particle change.