Motion graphsIB MYP Physics: Revision notes
Section 1
Distance-time graphs
A distance-time graph has time on the horizontal axis and distance on the vertical axis.
- A straight sloping line means constant speed.
- A steeper line means a greater speed.
- A horizontal (flat) line means the object is at rest: the distance is not changing.
- A curve means the speed is changing (a line that gets steeper means speeding up; one that flattens means slowing down).
The gradient = speed: gradient = change in distance ÷ change in time.
A flat line on a distance-time graph means the object is stopped, not moving at constant speed.
Section 2
Speed-time graphs
A speed-time (or velocity-time) graph has time on the horizontal axis and speed on the vertical axis.
- A horizontal line means constant speed (zero acceleration).
- A straight line sloping up means uniform acceleration.
- A straight line sloping down means uniform deceleration.
- A curve means the acceleration is changing.
- A line along the time axis (speed 0) means the object is at rest.
The gradient = acceleration: gradient = change in speed ÷ change in time.
A horizontal line on a speed-time graph means constant speed. It does not mean the object is stopped.
Section 3
Area under a speed-time graph
The area under a speed-time graph is the distance travelled.
- Rectangle: area = base × height = speed × time.
- Triangle: area = ½ × base × height.
For a more complicated shape, split it into rectangles and triangles, find each area, and add them.
Units: speed in m/s × time in s gives distance in metres.
Section 4
Calculating from straight-line graphs
Worked example: a car accelerates uniformly from rest to 10 m/s in 5 s, then travels at 10 m/s for 8 s.
- Acceleration (first 5 s) = gradient = 10 ÷ 5 = 2 m/s².
- Distance in first 5 s = area of triangle = ½ × 5 × 10 = 25 m.
- Distance in next 8 s = area of rectangle = 10 × 8 = 80 m.
- Total distance = 25 + 80 = 105 m.
- Average speed = total distance ÷ total time = 105 ÷ 13 = 8.1 m/s.
Write down which feature you are using: "gradient" for speed or acceleration, "area" for distance. Examiners award marks for naming it.
Section 5
Comparing the two graphs
| Distance-time graph | Speed-time graph | |
|---|---|---|
| Gradient | speed | acceleration |
| Area under graph | not used | distance |
| Horizontal line | at rest | constant speed |
| Straight sloping line | constant speed | uniform acceleration |
| Curve | changing speed | changing acceleration |
Always check the axis labels first, because the same shape means different things on each graph.
Must know
- Distance-time: gradient = speed; flat line = at rest; curve = changing speed.
- Speed-time: gradient = acceleration; flat line = constant speed; sloping line = uniform acceleration.
- Area under a speed-time graph = distance travelled (rectangles and triangles).
- Average speed = total distance ÷ total time.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Motion graphs
- A cyclist in Amsterdam rides along a straight cycle path. Her speed increases uniformly from 0 to 8 m/s in 4 s. She then rides at a constant 8 m/s for 10 s, before slowing down uniformly to rest in 6 s. A student draws a speed-time graph of her ride.State what the graph shows about her motion between 4 s and 14 s and explain how you can tell.2 marks
- A student in Doha walks along a straight road. She walks 120 m away from home in 80 s at a steady speed. She then stops at a friend's house for 40 s. She then walks a further 180 m in 90 s at a steady speed. A distance-time graph is drawn of her walk.Calculate her speed in the first part of the walk and use it to explain which of the two walking sections of the graph is steeper.2 marks
- A lorry sets off from rest on a straight, flat road in Nairobi. Its speed increases uniformly to 12 m/s in 6 s, and then stays constant at 12 m/s for a further 20 s. A speed-time graph is drawn of the lorry's journey.Calculate the distance the lorry travels in the first 6 s.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).