Interactive physics simulator
Acceleration-Time Graph
An acceleration-time graph shows how acceleration changes with time. The area under the graph gives the change in velocity.
Acceleration-Time Graph Simulator
Area under an acceleration-time graph gives change in velocity, not displacement.
Live Result
- Initial velocity
- 0 m/s
- Current velocity
- 0 m/s
- Final velocity
- 0 m/s
- Acceleration
- 0 m/s²
- Change in velocity
- 0 m/s
- Timer
- 0 s
- Total time
- 6 s
- Displacement
- 0 m
- Area under graph
- 0 m/s
- Direction
- zero acceleration
- Unit
- m/s²
- Formula
- Δv = area under graph
What is an Acceleration-Time Graph?
An acceleration-time graph compares acceleration with time. Time goes on the horizontal axis, acceleration goes on the vertical axis, and the signed area under the graph gives change in velocity.
Key Definition
An acceleration-time graph shows how acceleration changes with time.
- Time is shown on the horizontal x-axis.
- Acceleration is shown on the vertical y-axis.
- The area under the graph gives change in velocity.
- A line above zero means positive acceleration.
- A line at zero means zero acceleration.
- A line below zero means negative acceleration.
- Zero acceleration means velocity is constant, not always zero.
Acceleration-Time Graph Formula
Change in Velocity = Area under Acceleration-Time Graph
Δv = a x t
v = u + Δv
v = u + at for constant acceleration
s = ut + 1/2at² for constant acceleration
u is initial velocity, v is final velocity, a is acceleration, t is time, Δv is change in velocity, and s is displacement.
Use m/s² for acceleration, seconds for time, m/s for velocity, and meters for displacement.
What Different Lines Mean
Horizontal line above zero
Constant positive acceleration. Velocity changes in the positive direction.
Horizontal line at zero
Zero acceleration. Velocity stays constant, but the object may still be moving.
Horizontal line below zero
Constant negative acceleration. Velocity changes in the negative direction.
Area above time axis
Positive change in velocity.
Area below time axis
Negative change in velocity.
Changing acceleration line
Acceleration itself is changing. Area still gives change in velocity.
Real-life Example of an Acceleration-Time Graph
A small rocket has constant acceleration of 3 m/s² for 4 seconds.
Change in velocity = 3 x 4 = 12 m/s. If initial velocity is 0 m/s, final velocity is 12 m/s.
- An elevator capsule moving with zero acceleration keeps constant velocity.
- A ball slowing down has negative acceleration if its positive direction is upward.
Solved Examples
An acceleration-time graph shows constant acceleration of 4 m/s² for 5 s. Find change in velocity.
- Δv = a x t
- Δv = 4 x 5
- Δv = 20 m/s
Answer: 20 m/s
An object has initial velocity 3 m/s and acceleration 2 m/s² for 6 s. Find final velocity.
- v = u + at
- v = 3 + 2 x 6
- v = 15 m/s
Answer: 15 m/s
An acceleration-time graph shows acceleration of -2 m/s² for 4 s. Find change in velocity.
- Δv = a x t
- Δv = -2 x 4
- Δv = -8 m/s
- This means velocity decreases by 8 m/s in the positive direction.
Answer: -8 m/s
Common Mistakes
- Thinking area under acceleration-time graph gives displacement.
- Forgetting area gives change in velocity.
- Confusing acceleration-time graph with velocity-time graph.
- Thinking zero acceleration means object is stopped.
- Forgetting zero acceleration means velocity is constant.
- Ignoring negative acceleration below the time axis.
- Forgetting acceleration unit is m/s².
- Using graph slope instead of area for beginner-level questions.
Quick Summary
- Acceleration-time graph shows acceleration against time.
- x-axis shows time.
- y-axis shows acceleration.
- Area under graph gives change in velocity.
- Above the axis means positive change in velocity.
- Below the axis means negative change in velocity.
- Zero acceleration means velocity stays constant.
- For constant acceleration, Δv = at.
Practice Questions
1. Acceleration is 5 m/s² for 4 s. Find change in velocity.
Δv = a x t = 5 x 4 = 20 m/s.
2. Acceleration is -3 m/s² for 2 s. Find change in velocity.
Δv = -3 x 2 = -6 m/s.
3. What does the area under an acceleration-time graph represent?
The area represents change in velocity.
4. What does a horizontal line at zero acceleration mean?
Acceleration is zero, so velocity is constant.
5. An object has u = 2 m/s and a = 4 m/s² for 3 s. Find final velocity.
v = u + at = 2 + 4 x 3 = 14 m/s.
6. Does zero acceleration always mean the object is at rest?
No. It means velocity is not changing. The object may still move with constant velocity.
FAQ
Frequently Asked Questions
What is an acceleration-time graph?
An acceleration-time graph shows how acceleration changes with time.
What is shown on the x-axis of an acceleration-time graph?
Time is shown on the x-axis, usually in seconds.
What is shown on the y-axis of an acceleration-time graph?
Acceleration is shown on the y-axis, usually in meters per second squared.
What does the area under an acceleration-time graph represent?
The area under an acceleration-time graph represents change in velocity.
Does the area under an acceleration-time graph give displacement?
No. The area under an acceleration-time graph gives change in velocity, not displacement.
What does a horizontal line above zero mean?
It means constant positive acceleration.
What does a horizontal line at zero acceleration mean?
It means acceleration is zero, so velocity is constant.
Does zero acceleration mean the object is stopped?
No. Zero acceleration means velocity is not changing. The object may still be moving with constant velocity.
What does a line below the time axis mean?
It means negative acceleration, giving negative change in velocity.
How does the acceleration-time graph simulator work?
The simulator uses acceleration and time to calculate change in velocity. It also animates motion using velocity updated from the acceleration-time graph.
What is the formula for change in velocity from an acceleration-time graph?
For constant acceleration, change in velocity is Δv = a x t.
What happens if acceleration changes during motion?
If acceleration changes, the total change in velocity is found by adding the areas under each part of the acceleration-time graph.