The big idea: A velocity–time (v–t) graph shows how fast something is moving at each moment.
You read just two things off it:
- the slope of the line → the acceleration - the area under the line → the displacement (how far it travelled)
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How steep the line is tells you the acceleration. A steeper line → faster change in velocity. A flat (horizontal) line → no acceleration.
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On the velocity–time graph above the velocity rises from u = 4.0 m s⁻¹ to v = 20 m s⁻¹ over t = 8.0 s. Find the acceleration.
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The area between the line and the time-axis tells you the displacement — how far it went. For a straight line that area is just a triangle or trapezium.
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Using the same graph (u = 4.0 m s⁻¹, v = 20 m s⁻¹, t = 8.0 s), find how far the object travels.
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A falling line means slowing down: If the line slopes down, the slope is negative → the object is decelerating.
If the line dips below the time-axis, that area is negative → the object is moving backwards.
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Where it shows up: Motion graphs appear in every paper:
- Paper 1A (multiple choice) — read a slope or an area in one step. - Paper 1B (data) — plot points and find a gradient. - Paper 2 — determine_ the acceleration / distance, or sketch_ / describe_ the motion.
Three easy marks: (1) Say which rule you're using (slope or area). (2) Keep the unit on every line. (3) Watch the sign.
A car travelling at 24 m s⁻¹ brakes uniformly and stops in 6.0 s. (a) Find its acceleration. (b) Find the braking distance.
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