Motion graphsIB MYP Sciences: Revision notes
Section 1
Distance–time graphs
A distance–time graph has time on the horizontal axis and distance travelled on the vertical axis.
- A straight sloping line: constant speed.
- A horizontal line: the object is stationary (the distance is not changing).
- A steeper line: faster.
- A curve getting steeper: speeding up. A curve getting flatter: slowing down.
The graph tells you how far something has gone at each moment, not which direction it is moving.
A horizontal line on a distance–time graph means the object has stopped, not that it is moving at a steady speed.
Section 2
Speed from the gradient
The gradient (steepness) of a distance–time graph is the speed.
speed = gradient = change in distance ÷ change in time
Worked example: a line rises from 0 m at 0 s to 12 m at 8 s. Speed = 12 ÷ 8 = 1.5 m/s.
Choose two points on a straight section, work out the vertical change and the horizontal change, then divide.
Section 3
Velocity–time graphs
A velocity–time graph has time on the horizontal axis and velocity on the vertical axis.
- A horizontal line at a value above zero: constant velocity (acceleration is zero).
- A straight line sloping up: constant acceleration.
- A straight line sloping down: constant deceleration.
- A horizontal line on the time axis (velocity 0): the object is stationary.
The gradient of a velocity–time graph is the acceleration: a = change in velocity ÷ change in time.
Do not mix the graphs up. On a distance–time graph the gradient is speed. On a velocity–time graph the gradient is acceleration.
Section 4
Distance from the area
The area under a velocity–time graph is the distance travelled, because distance = velocity × time.
Split the graph into simple shapes:
- Rectangle: area = width × height
- Triangle: area = ½ × base × height
Worked example: a train accelerates from 0 to 20 m/s in 20 s. Distance = ½ × 20 × 20 = 200 m. If it then travels at 20 m/s for 60 s, that adds 20 × 60 = 1200 m.
Section 5
Describing and calculating from graphs
To describe motion, go section by section and say what the line is doing:
- Sloping up, straight: constant acceleration (speeding up at a steady rate)
- Horizontal: constant speed (or stationary on a distance–time graph)
- Sloping down, straight: constant deceleration
Back every description with numbers: read values, give the gradient with units, and include any distance from the area.
Worked example: a tram slows from 12 m/s to rest in 4 s. Deceleration = 12 ÷ 4 = 3.0 m/s².
Must Know
- Distance–time: gradient = speed; horizontal line = stationary
- Velocity–time: gradient = acceleration; area = distance
- Sloping straight line = constant speed (distance–time) or constant acceleration (velocity–time)
- Back every description with a calculation and units
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Motion graphs
- A student plots a distance–time graph for a toy robot moving along a straight corridor. The line rises in a straight slope from 0 m at 0 s to 12 m at 8 s, stays horizontal until 14 s, and then rises in a straight slope to 24 m at 20 s.Calculate the robot's speed between 14 s and 20 s.2 marks
- A tram in Istanbul leaves a stop. Its velocity–time graph is a straight line rising from 0 m/s at 0 s to 12 m/s at 6 s, then a horizontal line until 16 s, then a straight line falling to 0 m/s at 20 s.Describe, with a calculation, the motion of the tram between 16 s and 20 s.2 marks
- Priya, a student in Cape Town, investigates how the angle of a runway affects the acceleration of a trolley released from rest. A data logger plots a velocity–time graph for each run. She uses the same trolley and the same runway each time. Every graph is a straight line starting at the origin. The velocity after 1.0 s is 1.6 m/s for a runway angle of 10°, 3.2 m/s for 20° and 4.7 m/s for 30°.Identify the independent variable, the dependent variable and one variable that Priya must control.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).