1.2.1Dynamics

Velocity–Time Graphs

5 min read 6 parts Lesson 6 of 22

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Section 1 of 6Reading the Axes

A velocity–time graph is a picture of a whole journey, and each straight section tells you a different story about the motion.

Vertical axis

Velocity (or speed) is plotted upwards on the y-axis, because it is the quantity that depends on time.

Horizontal axis

Time is plotted along the x-axis, and the graph is read from left to right as the journey proceeds.

Speed–time graph

A speed–time graph can only show positive values because speed is a scalar with no direction.

Velocity–time graph

A velocity–time graph can go below the axis, where a negative value means motion in the opposite direction.

Section 2 of 6Shapes and What They Mean

Shapes and What They Mean

Horizontal line on the axis

The velocity is zero for that period, so the object is at rest and not moving at all.

Horizontal line above the axis

The velocity is steady and not changing, so the object moves with constant velocity and has zero acceleration.

Straight line sloping up

The velocity increases by the same amount every second, which is constant acceleration.

Straight line sloping down

The velocity decreases steadily, which is constant deceleration, and a line crossing the axis shows a reversal.

Graph section	Motion	Acceleration
Flat at zero	At rest	Zero
Flat above zero	Constant velocity	Zero
Rising line	Speeding up	Positive
Falling line	Slowing down	Negative

Section 3 of 6Describing a Journey

Start at the left of the graph and identify each straight section in order.

For each section decide whether the line is flat, rising or falling, and say what the object is doing.

Quote values from the graph, for example speeding up from 0 to 12 m/s over the first 4 seconds.

Notice any point where the line crosses the time axis, since the object has stopped and then changes direction there.

Section 4 of 6Steepness

Steepness

Steep line

A steep slope means the velocity changes quickly, so the acceleration or deceleration is large.

Gentle line

A shallow slope means the velocity changes slowly, so the acceleration is small.

Curve

A curved line means the acceleration itself is changing; at National 5 this is described qualitatively only.

Section 5 of 6Worked Example

Question

A car starts from rest, speeds up to 12 m/s in 4 s, travels at 12 m/s for 6 s, then brakes to a stop in 2 s.
Describe each section of its velocity–time graph.

0 to 4 s: a straight line rising from 0 to 12 m/s, so constant acceleration.
4 s to 10 s: a horizontal line at 12 m/s, so constant velocity with zero acceleration.
10 s to 12 s: a straight line falling from 12 m/s to 0,
- so constant deceleration; this section is steeper than the first because the speed drops in less time.

Answer Speeding up for 4 s, constant velocity for 6 s, then slowing down to rest in 2 s.

Section 6 of 6Exam Checklist & Tips

1.2.1 – Key Points for the Exam

Velocity–time graph A graph that shows how velocity changes with time.
Constant velocity Motion at the same speed in the same direction.
Deceleration A negative acceleration in which the object slows down.
Gradient The steepness of a graph line.

Common Mistakes

Reading a flat line on a velocity–time graph as the object being at rest;
- it is at rest only if the line is on the axis.
Confusing a velocity–time graph with a distance–time graph, where flat means stopped.
Thinking a falling line always means the object is moving backwards;
- it may just be slowing down while still above the axis.
Forgetting to quote values and units when asked to describe the motion.

Physics 0625 & 9702 SUVAT Mastery Graph Interpretation

Constant Acceleration Equations (SUVAT) & Slopes

v = u + at | s = ut + ½at² | v² = u² + 2as | s = ½(u + v)t

Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
Free Fall in vacuum: a = g ≈ 9.81 m/s² downwards (air resistance negligible).