GCSE · Physics · Edexcel · Spec 1PH0

Velocity/time graphs

On a distance–time graph a flat line means stopped. On a velocity–time graph, the same flat line could be a car cruising down a motorway.

A tram's journey from one stop to the next

Time (s): 20. Velocity (m/s): 15

slide me along the line

Exam line: Steeper line, bigger acceleration. Flat line, steady velocity. Sloping down, slowing down.

Check your thinking

What does the flat line mean?

Between 15 s and 27 s the tram's line is flat, sitting at 15 m/s.

What is the tram doing during those 12 seconds?

It has stopped. A flat line means nothing is happening.It's speeding up steadily. The line is at its highest there.It's moving at a steady 15 m/s. Its velocity isn't changing.It's slowing down. The line has stopped going up.

How sure are you?

I'm sureI think soI'm guessing

It has stopped. A flat line means nothing is happening.

This is a common misconception

That's the rule for a distance–time graph, where a flat line means the distance isn't changing. This graph plots velocity, and the line is sitting at 15 m/s — so the tram is still covering 15 metres every second. Stationary means the velocity is zero. On a velocity–time graph that is a line lying along the time axis, like the tram after 32 s.

It's speeding up steadily. The line is at its highest there.

This is a common misconception

Height tells you how fast the tram is going, not whether it is getting faster. Speeding up needs the velocity to change, and here it stays at 15 m/s the whole time. The speeding up happened earlier, while the line was climbing.

It's moving at a steady 15 m/s. Its velocity isn't changing.

This matches the evidence

Exactly. Flat line means the velocity isn't changing: constant velocity and zero acceleration. The tram is cruising, not parked.

It's slowing down. The line has stopped going up.

This is a common misconception

Slowing down means the velocity drops, and the line would slope downwards, as it does from 27 s to 32 s. Here the velocity holds at 15 m/s. What has dropped to zero is the acceleration, not the velocity.

On a velocity–time graph, flat means steady velocity. Stationary is the flat line at zero, lying along the time axis.

Your turn to finish it

Acceleration from the gentle climb

Use the tram's graph to find its acceleration between 5 s and 15 s.

Acceleration is the gradient of the line: change in velocity ÷ time taken. As an equation, a = (v − u) ÷ t, where u is the velocity at the start of the section and v is the velocity at the end.The line is straight here, so the acceleration is the same all the way along this section.
missing step

Which line is step 2?

Read the velocities at the ends of the section: at 5 s, u = 10 m/s; at 15 s, v = 15 m/s.Read the velocities: u = 0 m/s, because the tram started from rest; v = 15 m/s.Read the values: u = 5 m/s, where the section starts; v = 15 m/s.

Predict, then check

Now switch from the slope of the line to the space underneath it.

From 15 s to 27 s the tram cruises at a steady 15 m/s. How far does it travel in those 12 seconds?

Distance from the area

Problem

How far does the tram travel in the first 15 s of its journey?

Spot the lost mark

Check this answer

A cyclist starts from rest and speeds up steadily to 8 m/s in 4 s. She then rides at a steady 8 m/s for 6 s more. Using the area under her velocity–time graph, find the total distance she travels in the 10 s.

A student's answer — which line goes wrong?

Split the area under the line: a triangle from 0 s to 4 s, and a rectangle from 4 s to 10 s.
Triangle: 4 × 8 = 32 m
Rectangle: base = 10 − 4 = 6 s, so area = 6 × 8 = 48 m
Total distance = 32 + 48 = 80 m

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

The slope tells you the acceleration. The space underneath tells you how far.

What you need to know

A velocity–time graph has velocity on the vertical axis and time on the horizontal axis, so it shows how the velocity changes during the motion.
The gradient (slope) of a velocity–time graph is the acceleration: acceleration = change in velocity ÷ time taken for that change.
A steeper line means a bigger acceleration. A horizontal line means constant velocity (zero acceleration). A line sloping downwards means the object is decelerating.
For a straight sloping section, a = (v − u) ÷ t: read the start velocity u, the end velocity v and the time interval t off the axes. Acceleration is in m/s².
The distance travelled is the area between the line and the time axis. Split it into rectangles (base × height) and triangles (½ × base × height), using time in s and velocity in m/s, to get metres.
A horizontal line on a velocity–time graph means moving at constant velocity, not stationary. A stationary object has a line along the time axis (velocity zero).

The big picture

A velocity–time graph shows how an object's velocity changes over time, with velocity up the side and time along the bottom. The gradient of the line is the acceleration: a steeper line means a bigger acceleration, a flat line means constant velocity, and a line sloping down means the object is decelerating. For a straight section, acceleration = change in velocity ÷ time taken, in m/s². The area under the line is the distance travelled: split it into rectangles and triangles, use seconds and m/s, and the answer comes out in metres. A flat line does not mean stopped — a stationary object has a line along the time axis.

Key points

1Ask of every section: what is the velocity doing — rising, steady or falling?

2Slope = acceleration. Steeper means the velocity is changing faster.

3a = (v − u) ÷ t, using the time the change took, not a clock reading. Units: m/s².

4Area under the line = distance. Rectangles are base × height; triangles need the ½.

5Flat line = cruising. Line along the time axis = standing still.

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Worked example

Problem

At the end of its journey the tram brakes steadily from 15 m/s at 27 s to a stop at 32 s. Find its acceleration while braking, and how far it travels while braking.

⚠ Watch out

Reading a velocity–time graph as if it were a distance–time graph. A flat line here does not mean the object has stopped — it means it is moving at a constant velocity. Only a line along the time axis (velocity zero) means stationary.

🧠

Memory hook

Slope for speeding up, space for how far. The SLOPE of the line tells you the acceleration; the SPACE underneath it tells you the distance.

✓

Check yourself

Cover the page and sketch a velocity–time graph for a bike that speeds up, cruises, then brakes to a stop. Where is the acceleration zero? Shade the distance travelled.

Flashcards

(13)

What goes on each axis of a velocity–time graph?

Velocity up the vertical axis, time along the horizontal axis.

What does the gradient of a velocity–time graph tell you?

The acceleration.

Write the equation for acceleration from a change in velocity.

a = (v − u) ÷ t, where u is the initial velocity, v the final velocity and t the time taken for the change.

What is the unit of acceleration?

Metres per second squared, m/s².

Two sloping sections: one steep, one gentle. Which has the bigger acceleration?

The steeper one — its velocity changes more in each second.

A horizontal line on a velocity–time graph means…?

Constant velocity: the object is moving, with zero acceleration.

A line sloping downwards on a velocity–time graph means…?

The velocity is falling: the object is decelerating (negative gradient).

How does a velocity–time graph show an object that is stationary?

A line along the time axis, because the velocity is zero.

What does the area under a velocity–time line give you?

The distance travelled.

Why does the area under a velocity–time line equal the distance?

For a rectangle, width × height is time × velocity, and velocity × time is distance.

Area of a triangle under the line?

½ × base × height — don't drop the ½.

Time in s and velocity in m/s. What unit is the area in?

Metres (m).

Reading t for one section of the graph: what do you do?

Subtract the time at the start of the section from the time at the end.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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A tram's journey from one stop to the next

What does the flat line mean?

Acceleration from the gentle climb

Check this answer

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