Physics
Physics
Problem
A body moves in a straight line with constant acceleration . (i) Starting from the basic kinematic relations, derive an expression for the average velocity of the body between times and . (ii) Show that this average velocity equals the instantaneous velocity at any instant within the interval only when . (iii) Using your result, explain what distinctive feature of a velocity–time graph indicates that the motion is uniform.Intuitive explanation
Average velocity under constant acceleration is simply the arithmetic mean of the initial and final velocities over an interval—a consequence of how linearly velocity changes with time. The key insight is recognizing that this average equals the instantaneous velocity at the midpoint of the interval only when acceleration is zero, which reveals why uniform motion produces a special graph feature: a horizontal line where velocity never changes.
Intuitive explanation
Average velocity under constant acceleration is simply the arithmetic mean of the initial and final velocities over an interval—a consequence of how linearly velocity changes with time. The key insight is recognizing that this average equals the instantaneous velocity at the midpoint of the interval only when acceleration is zero, which reveals why uniform motion produces a special graph feature: a horizontal line where velocity never changes.