The shape of a velocity-time graph
Level, rising or falling lines.
Three cars
One car cruises at a steady velocity on a highway. One starts from rest and speeds up. One is moving and slows down to a stop.
Do you think their velocity-time graphs have different shapes?
What this lesson covers
The idea
A velocity-time graph parallel to the time axis means constant velocity and zero acceleration; a straight line rising or falling means velocity increasing or decreasing with constant acceleration.
Three cars
One car cruises at a steady velocity on a highway. One starts from rest and speeds up. One is moving and slows down to a stop.
Do you think their velocity-time graphs have different shapes?
- Yes, each one has its own shape
- No, the three graphs look the same
- Just the car that stops has a graph
Three graphs
Open each tab and read the shape.
Shape tells the acceleration
The level line meant the velocity did not change: zero acceleration. The rising line meant the velocity grew by equal amounts in equal times, and the falling line that it shrank by equal amounts.
A velocity-time graph parallel to the time axis means constant velocity and zero acceleration. A straight line rising or falling means the velocity is increasing or decreasing with constant acceleration.
Notes
Level line: constant velocity, zero acceleration. Straight rising or falling line: velocity increasing or decreasing with constant acceleration.
Check yourself
A velocity-time graph is a straight line parallel to the time axis. This shows that…
A velocity-time graph is a straight line rising. The car's velocity is…
A velocity-time graph is a straight line falling. The acceleration is…
Table 4.6 gives a car's velocity as 15.0, 12.5, 10.0, 7.5 m s⁻¹ at 0, 5, 10, 15 s. Its velocity-time graph is…
- the car is speeding up. A rising line, not a level one, shows the velocity increasing.
- the acceleration is large. A level line means the velocity does not change, so the acceleration is zero.
- the velocity is constant and the acceleration is zero — correct. Yes!
- increasing with constant acceleration — correct. Yes!
- constant, with zero acceleration. A level line shows constant velocity. A rising line shows the velocity changing.
- decreasing with constant acceleration. A falling line, not a rising one, shows a decreasing velocity.
- zero. The velocity changes, so the acceleration is not zero.
- constant, and opposite to the direction of velocity — correct. Yes!
- constant, and in the direction of velocity. That is the case of a rising line, where the velocity increases.
- a straight line rising. The velocity is getting smaller, so the line falls.
- a line parallel to the time axis. The velocity is not constant, so the line is not level.
- a straight line falling — correct. Yes!