The slope of a straight-line velocity-time graph represents

Analyze the question: You are asked what the slope (gradient) of a straight-line velocity-time graph represents.

Concept: The slope of any graph is the change in the y-quantity divided by the change in the x-quantity.

For a velocity-time graph:

• y-axis = velocity (v)
• x-axis = time (t)

Solution:

Slope = Δv / Δt = (change in velocity) / (time taken)

This is the definition of acceleration.

A straight line means the slope is constant. So the acceleration is constant, which is uniform acceleration.

Checking the options:

• A. Uniform acceleration: Correct. A constant slope means a constant rate of change of velocity.
• B. Uniform speed: Wrong. Uniform speed would show as a horizontal line, with zero slope.
• C. Total distance travelled: Wrong. Distance is the area under the velocity-time graph, not the slope.
• D. Work done: Wrong. Work done is not found from the slope of a velocity-time graph.

Tip: Remember this pair for velocity-time graphs:

• Slope = acceleration
• Area under the graph = distance (displacement)

A horizontal line means constant velocity (zero acceleration). A straight sloping line means uniform acceleration. A curve means changing acceleration.