An acceleration-time graph shows how an object's acceleration changes as time passes. It is important because acceleration controls how velocity changes, including speeding up, slowing down, or changing direction. Reading these graphs helps connect motion diagrams, equations, and real-world motion such as cars, elevators, and falling objects.
The sign and shape of the graph tell you what is happening to the velocity at each moment.
The area between an acceleration-time graph and the time axis gives the change in velocity, written as Δv = area under a-t graph. A positive area increases velocity, while a negative area decreases velocity. A zero acceleration line means velocity is constant, not necessarily zero.
By connecting acceleration-time, velocity-time, and position-time graphs, you can describe motion more completely.
Key Facts
- Area under an acceleration-time graph gives change in velocity: Δv = ∫ a dt.
- For constant acceleration, Δv = aΔt.
- Positive acceleration means velocity increases in the positive direction.
- Negative acceleration means velocity changes in the negative direction, which may mean slowing down or speeding up backward.
- Zero acceleration means constant velocity: a = 0, so Δv = 0 over that interval.
- Acceleration is the slope of a velocity-time graph: a = Δv / Δt.
Vocabulary
- Acceleration
- Acceleration is the rate at which velocity changes with time.
- Acceleration-time graph
- An acceleration-time graph plots acceleration on the vertical axis and time on the horizontal axis.
- Change in velocity
- Change in velocity is the final velocity minus the initial velocity, written as Δv = vf - vi.
- Area under the curve
- The area under an acceleration-time graph represents the change in velocity during a time interval.
- Constant velocity
- Constant velocity means an object moves with the same velocity because its acceleration is zero.
Common Mistakes to Avoid
- Thinking the height of an acceleration-time graph is velocity. The height shows acceleration, while the area under the graph shows change in velocity.
- Assuming zero acceleration means the object is stopped. Zero acceleration means velocity is not changing, so the object may still be moving.
- Ignoring negative area below the time axis. Area below the axis gives a negative change in velocity and must be subtracted from positive area.
- Calling negative acceleration always slowing down. Negative acceleration slows an object only if its velocity is positive, but it speeds up an object moving in the negative direction.
Practice Questions
- 1 An object has a constant acceleration of 3.0 m/s² from t = 0 s to t = 4.0 s. What is its change in velocity during this interval?
- 2 A car starts with velocity 12 m/s. Its acceleration is -2.0 m/s² for 5.0 s, then 0 m/s² for 3.0 s. What is its final velocity?
- 3 An acceleration-time graph is above the time axis from 0 to 2 s, on the time axis from 2 to 5 s, and below the time axis from 5 to 7 s. Explain how the velocity changes in each interval.