A position-time graph of a cyclist on a straight road is a straight line sloping down.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A position-time graph of a cyclist on a straight road is a straight line sloping down. Asha says: "The line goes down, so the cyclist is riding downhill." Ravi says: "The line goes down, so the cyclist is slowing down."
Who is right? Explain what the graph really shows.
Need a reminder? The key ideaShow
A position-time graph shows where a body is at each time. Its slope is the velocity. It is not a picture of the path.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Read the slope, not the shape of the line as if it were a hill.
Step 1. Asha. Wrong. The graph is not a picture of the road. The road could be perfectly flat; the graph only shows position against time.
Step 2. Ravi. Wrong. A straight line has a constant slope, so the velocity is constant: the cyclist is neither slowing down nor speeding up.
Step 3. What it shows. The slope is negative, so the velocity is negative: the cyclist moves at a steady speed towards smaller , back towards the origin.
Answer: Neither. The cyclist moves at a steady speed in the negative direction.
Watch out. On a velocity-time graph a falling line would mean slowing down (while above the axis). Always check which graph you are reading.
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