Learn how to interpret, analyse, and sketch displacement-time, velocity-time, and acceleration-time graphs to determine physical quantities of linear motion.
Interpreting gradient and area to connect displacement, velocity and acceleration.
The gradient of a displacement-time graph gives velocity. The gradient of a velocity-time graph gives acceleration. The area under a velocity-time graph gives displacement.
Key relationships
Displacement-time graph \(\xrightarrow{\text{gradient}}\) Velocity-time graph \(\xrightarrow{\text{gradient}}\) Acceleration-time graph.
Reverse direction: the area under an acceleration-time graph gives the change in velocity \(\Delta v\). Combine it with the initial velocity \(v_0\) to determine velocity. Then, the area under a velocity-time graph gives the change in displacement \(\Delta s\), which is combined with the initial displacement \(s_0\) to determine absolute displacement.
How to read and use the three main linear motion graphs.
The gradient gives velocity. A horizontal line means the object is at rest. A straight diagonal line means uniform velocity. A curve curving upward means acceleration.
The gradient gives acceleration. The area under the graph gives displacement. A horizontal line means uniform velocity and zero acceleration.
A line on the time axis means zero acceleration. A horizontal line above or below the axis means uniform acceleration. An upward-sloping line means increasing acceleration, while a downward-sloping line means decreasing acceleration.
Areas above the time axis represent positive displacement. Areas below the time axis represent negative displacement. For total distance, treat all areas as positive.
Answer in your mind, then press “Check Answer”.
What does the gradient of a displacement-time graph represent?
How can displacement be determined from a velocity-time graph?
What does a horizontal line on a velocity-time graph indicate about the acceleration of the object?
A downward-sloping straight line on a displacement-time graph means the object is decelerating.
A downward straight line on an \(s-t\) graph has a constant negative gradient, which means the object is moving at a uniform velocity in the negative direction.
Distance and displacement obtained from a velocity-time graph are always the same.
Distance is the total area without regard to sign, whereas displacement considers direction where areas below the axis are subtracted.
Objective: Interpret motion graphs and identify the physical quantities they represent.
1 Which physical quantity is represented by the gradient of a velocity-time graph?
2 Based on a velocity-time graph, what does the area under the graph representing a region below the time axis indicate?
3 The gradient of a displacement-time graph gives the of the object.
4 On a velocity-time graph, a horizontal straight line with zero gradient indicates that the object has acceleration.
Drag each graphical feature to the correct meaning. If using a phone, tap the answer first, then tap the matching box.
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