Step 1: Understanding the Concept:
We are given that force (and thus acceleration) is perpendicular to velocity.
\( \vec{F} \perp \vec{v} \implies \vec{a} \perp \vec{v} \).
This means the force does no work on the particle.
Step 2: Key Formula or Approach:
Work-Energy Theorem: Power \( P = \vec{F} \cdot \vec{v} \).
If \( \vec{F} \perp \vec{v} \), then \( P = 0 \).
\( P = \frac{dK}{dt} = 0 \), where \( K \) is kinetic energy.
Step 3: Detailed Explanation:
Since \( \vec{F} \cdot \vec{v} = 0 \), the rate of change of kinetic energy is zero.
\( \frac{d}{dt} (\frac{1}{2} mv^2) = 0 \).
This implies the magnitude of velocity (speed) is constant, and hence kinetic energy is constant.
Velocity vector changes direction (uniform circular motion is an example), so velocity is not constant.
Acceleration direction changes (always towards center in UCM), so acceleration is not constant vector-wise (though magnitude might be).
Linear momentum \( \vec{p} = m\vec{v} \) changes direction, so it's not constant.
Step 4: Final Answer:
The kinetic energy is constant.