lesson
Gradient and area answer different questions
1 · Learn
On a velocity-time graph, gradient gives acceleration and signed area gives displacement. A straight sloping segment indicates constant acceleration. If velocity changes sign, displacement and total distance need not agree.
Read axis units and scale. A graph height is velocity, not acceleration, and a horizontal line can represent non-zero constant motion.
2 · Worked example
Velocity rising from 2 to 10 m/s in 4 s gives acceleration 2 m/s². The trapezium area is average velocity 6 × 4 = 24 m displacement.
3 · Your turn
Velocity rises uniformly from 0 to 6 m/s in 3 s. Find acceleration and displacement.
Check your answer
2 m/s² and 9 m.
4 · Apply your learning
Calculate gradient and area separately on a supplied graph and explain their units.
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Check a calculation · Year 5 onward
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Powers, roots and trigonometry · Year 7 onward
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