The average speed of an object is determined by dividing the sum of its initial and final speeds by two only when the acceleration is

Analyze the question: We're asked when average speed = (initial speed + final speed) / 2, that is, (u + v)/2.

Explain the concept: This formula comes from the equations of motion for constant acceleration. If acceleration is uniform, speed changes at a steady rate, so it increases (or decreases) linearly with time. For a linear change, the average value is simply the midpoint of the start and end values.

Show the solution:

For uniform acceleration a:

• v = u + at
• s = ut + ½at²

Average speed = s / t = u + ½at

Substitute at = v − u:

Average speed = u + ½(v − u) = (u + v) / 2

This derivation depends on a being constant. If acceleration were changing, increasing, or decreasing, the speed-time graph would be curved, and the average would not be the midpoint of u and v. The area under the graph would not be a simple trapezium.

Check the options:

• A. Changing: the speed-time graph is curved, so the formula fails.
• B. Uniform: the graph is a straight line, so the formula works.
• C. Increasing: acceleration that is itself increasing gives a curve, so the formula fails.
• D. Decreasing: likewise a curve, so the formula fails.

**Answer: B (uniform).

Tip: Remember that (u + v)/2 is the area of a trapezium on a speed-time graph divided by time. It only works when the top edge is a straight line, meaning constant (uniform) acceleration. Whenever you see the formulas v = u + at or s = ½(u + v)t, think "constant acceleration."