Question

an object moves under the influence of a single force of constant magnitude. the objects kinetic energy is constant throughout its motion. which of the following statements is a correct claim about this force?
a the directions of the force and velocity are the same as each other.
b the directions of the force and velocity are opposite to each other.
c the directions of the force and velocity are perpendicular to each other.
d the directions of the force and velocity are neither parallel nor perpendicular to each other.

Explanation:

Step1: Recall the work - kinetic energy theorem

The work - kinetic energy theorem states that \(W=\Delta K\), where \(W\) is the work done by the force and \(K\) is the kinetic energy. Given that \(K\) is constant, so \(\Delta K = 0\), then \(W=0\).

Step2: Recall the formula for work

The formula for work is \(W = Fd\cos\theta\), where \(F\) is the magnitude of the force, \(d\) is the displacement, and \(\theta\) is the angle between the force \(\vec{F}\) and the displacement \(\vec{d}\). Since \(W = 0\) and \(F
eq0\), \(d
eq0\) (the object is moving), then \(\cos\theta=0\).

Step3: Solve for the angle \(\theta\)

If \(\cos\theta = 0\), then \(\theta = 90^{\circ}\). When the object is moving, the direction of the displacement is the same as the direction of the velocity (for a small time interval \(v=\frac{d}{t}\), direction of \(d\) and \(v\) is the same). So the angle between the force and the velocity is \(90^{\circ}\), which means the force and velocity are perpendicular.

Answer:

C. The directions of the force and velocity are perpendicular to each other.