Interactive physics simulator
Velocity-Time Graph
A velocity-time graph shows how an object's velocity changes with time. The slope of the graph shows acceleration, and the area under the graph shows displacement.
Velocity-Time Graph Simulator
Slope shows acceleration. Area under the velocity-time graph shows displacement.
Live Result
- Initial velocity
- 0 m/s
- Current velocity
- 0 m/s
- Final velocity
- 0 m/s
- Acceleration
- 0 m/s²
- Timer
- 0 s
- Total time
- 6 s
- Displacement
- 0 m
- Graph slope
- 0 m/s²
- Area under graph
- 0 m
- Direction
- rest
- Unit
- m/s
- Formula
- a = Δv / Δt
What is a Velocity-Time Graph?
A velocity-time graph compares velocity with time. Time goes on the horizontal axis, velocity goes on the vertical axis, the slope gives acceleration, and the signed area under the graph gives displacement.
Key Definition
A velocity-time graph shows how velocity changes with time.
- Time is shown on the horizontal x-axis.
- Velocity is shown on the vertical y-axis.
- Slope of the graph shows acceleration.
- Area under the graph shows displacement.
- Horizontal line means constant velocity.
- Line at zero means the object is at rest.
- Line below the time axis means velocity is negative.
Velocity-Time Graph Formula
Acceleration = Change in Velocity / Change in Time
a = Δv / Δt
Displacement = Area under Velocity-Time Graph
s = vt for constant velocity
s = ((u + v) / 2) x t for constant acceleration
v = u + at
u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement.
Use m/s for velocity, seconds for time, m/s² for acceleration, and meters for displacement.
What Different Lines Mean
Horizontal line above zero
Constant positive velocity. Acceleration is zero and the object moves forward steadily.
Upward sloped line
Velocity increases. The slope is positive acceleration.
Downward sloped line
Velocity decreases. Acceleration is negative and the object may slow down or reverse.
Line on zero
Velocity is zero. The object is at rest.
Line below zero
Velocity is negative. The object moves in the negative direction.
Crossing the time axis
Velocity changes sign, so the object changes direction.
Real-life Example of a Velocity-Time Graph
A small rocket starts from rest and speeds up at 2 m/s² for 5 seconds.
Final velocity = 0 + 2 x 5 = 10 m/s. Displacement = 1/2 x 2 x 5² = 25 m.
- A train capsule moving at constant velocity creates a horizontal line.
- An elevator capsule slowing down creates a downward sloped line.
Solved Examples
A velocity-time graph shows velocity increasing from 0 m/s to 20 m/s in 5 s. Find acceleration.
- a = Δv / Δt
- a = (20 - 0) / 5
- a = 4 m/s²
Answer: 4 m/s²
A graph has constant velocity of 6 m/s for 4 s. Find displacement.
- Displacement = area under graph
- s = v x t
- s = 6 x 4 = 24 m
Answer: 24 m
Velocity changes from 10 m/s to 0 m/s in 5 s. Find acceleration and displacement.
- Acceleration = (0 - 10) / 5 = -2 m/s²
- Displacement = ((10 + 0) / 2) x 5
- Displacement = 25 m
Answer: -2 m/s² and 25 m
Common Mistakes
- Confusing velocity-time graph with distance-time graph.
- Thinking slope means speed instead of acceleration.
- Forgetting area under graph means displacement.
- Ignoring negative velocity below the time axis.
- Treating area below the axis as positive displacement.
- Forgetting horizontal line means constant velocity, not rest unless velocity is zero.
- Confusing displacement with distance traveled.
- Forgetting units: acceleration is m/s² and displacement is meters.
Quick Summary
- Velocity-time graph shows velocity against time.
- x-axis shows time.
- y-axis shows velocity.
- Slope shows acceleration.
- Area under graph shows displacement.
- Horizontal line means constant velocity.
- Line at zero means rest.
- Crossing the axis means direction changes.
Practice Questions
1. Velocity increases from 0 m/s to 15 m/s in 5 s. Find acceleration.
a = (15 - 0) / 5 = 3 m/s².
2. Velocity is constant at 8 m/s for 6 s. Find displacement.
s = v x t = 8 x 6 = 48 m.
3. What does the slope of a velocity-time graph represent?
The slope represents acceleration.
4. What does the area under a velocity-time graph represent?
The area represents displacement.
5. What does a horizontal line at 5 m/s mean?
The object has constant velocity of 5 m/s and zero acceleration.
6. What does a line below the time axis mean?
The object has negative velocity and moves in the negative direction.
FAQ
Frequently Asked Questions
What is a velocity-time graph?
A velocity-time graph shows how an object’s velocity changes with time.
What is shown on the x-axis of a velocity-time graph?
Time is shown on the x-axis, usually in seconds.
What is shown on the y-axis of a velocity-time graph?
Velocity is shown on the y-axis, usually in meters per second.
What does the slope of a velocity-time graph represent?
The slope of a velocity-time graph represents acceleration.
What does the area under a velocity-time graph represent?
The area under a velocity-time graph represents displacement.
What does a horizontal line mean on a velocity-time graph?
A horizontal line means constant velocity. It means acceleration is zero.
What does a line at zero velocity mean?
A line at zero velocity means the object is at rest.
What does a line below the time axis mean?
It means the object has negative velocity and is moving in the negative direction.
What does it mean when the graph crosses the time axis?
It means velocity changes sign, so the object changes direction.
How does the velocity-time graph simulator work?
The simulator uses velocity and time values to animate object motion, calculate acceleration from slope, and calculate displacement from the area under the graph.
Is area below the time axis positive or negative?
Area below the time axis represents negative displacement.
Does a horizontal line always mean the object is at rest?
No. A horizontal line means constant velocity. The object is at rest only if the horizontal line is at zero velocity.