Displacement-Time Graphs
Displacement-Time Graphs
- A displacement-time (s-t) graph shows where an object is at every moment.
- One rule gives you the whole graph: the equals the velocity.
Reading straight sections
- Gradient means rise over run. Here the rise is displacement and the run is time, so gradient = = velocity. That is exactly the definition from the last lesson.
- A steep line means fast. A flat line means not moving. A line sloping down means moving back toward the start.
Worked example
Warm-up: velocity from a straight section
On an s-t graph, a straight section rises from 0 m to 24 m between t = 0 and t = 8.0 s. Find the velocity.
- Gradient: .
Answer
On an s-t graph, read the slope, never the height. A high flat line means far away and not moving.
A curved graph: use a tangent
- A curved s-t graph means the velocity is changing: the gradient is different at every point.
- To find the velocity at one instant, draw a at that point and take the tangent's gradient. That gradient is the instantaneous velocity from lesson 2.1.
Worked example
A harder step: instantaneous velocity from a tangent
On the curve above, a tangent is drawn at t = 4.0 s. It passes through (2.0 s, 0 m) and (6.0 s, 16 m). Find the velocity at t = 4.0 s.
- Rise and run of the tangent: , .
- .
Answer
- Common exam versions of this graph: pick the description that matches a given s-t shape, compare two objects on one graph (they meet where the lines cross), or read an instantaneous velocity from a tangent.
Common mistake
Use two points that are far apart on the tangent line, not two points on the curve. Points on the curve give an average velocity, not the velocity at that instant.