Enter graph and object data
Enter each straight section of the force-time graph. Negative force values are allowed.
Formula used
For each straight graph segment, the impulse is:
Jᵢ = ((Fstart + Fend) ÷ 2) × Δt
The total impulse is the sum of all segment impulses:
Jtotal = ΣJᵢ
Impulse equals the change in momentum:
Jtotal = m(vfinal − vinitial)
Rearrange it for final velocity: vfinal = vinitial + Jtotal ÷ m. Final speed equals the magnitude of final velocity.
How to use this calculator
- Enter the object's mass and choose its mass unit.
- Enter initial velocity. Use a negative value for opposite motion.
- Select the units shown on the force-time graph axes.
- Enter one row for every straight graph interval.
- Use graph endpoint values for each start and end force.
- Add another row whenever the graph slope changes.
- Choose an output speed unit and calculate the result.
- Review final velocity, final speed, net impulse, and direction.
Example graph data
This example uses a 2 kg object that starts from rest.
| Segment | Duration (s) | Start force (N) | End force (N) | Impulse (N s) |
|---|---|---|---|---|
| 1 | 2 | 0 | 10 | 10 |
| 2 | 3 | 10 | 10 | 30 |
| 3 | 1 | 10 | 0 | 5 |
| Total impulse | 45 | |||
The final velocity is 0 + 45 ÷ 2 = 22.5 m/s. The final speed is 22.5 m/s.
Reading a force-time graph
Understanding a Force-Time Graph
A force-time graph shows how an external force changes during motion. Time is on the horizontal axis. Signed force is on the vertical axis. The area below the plotted line matters most. This area is called impulse. Impulse changes an object's momentum. Momentum depends on mass and velocity. A large force may act briefly. Both can create equal impulse. This is why the graph shape matters. The calculator reads each straight graph section. It uses its duration and endpoint forces. It adds every segment area precisely for each calculation. The total can be positive, negative, or zero.
Impulse Creates Velocity Change
For constant force, impulse equals force multiplied by time. Sloping straight sections form trapezoids on the graph. Their area uses the mean endpoint force. That average is multiplied by section duration. The result is segment impulse. All segment impulses are then added. Newton's second law connects impulse and momentum change. The relation is J equals m times velocity change. Final velocity equals initial velocity plus impulse divided by mass. The displayed speed is the absolute velocity magnitude. A negative result points opposite the chosen direction. The calculator also shows total time, average force, and average acceleration.
Choosing Useful Inputs
Start by entering the object's mass. Select kilograms, grams, or pounds-mass carefully. Next enter the initial velocity and unit. Use a negative value for opposite motion. Every graph section needs a positive duration. Force entries may be positive or negative. Add the start and end force values. A horizontal section uses equal force values. A triangular pulse starts or ends at zero. Split the graph wherever its slope changes. More sections improve curved graph approximations. The calculator converts inputs into SI units internally. Confirm that graph labels match selected units. Milliseconds and minutes strongly affect impulse.
Interpreting the Result
Final speed tells how fast the object moves afterward. Final velocity also reports direction. Compare it with starting velocity. This reveals slowing, stopping, or reversal. A negative impulse slows positive motion. It can stop the object completely. Further negative impulse reverses its direction. Positive impulse does the opposite. Average force equals total impulse divided by total time. It summarizes the complete force history. Average acceleration summarizes the velocity change. Instantaneous acceleration can differ. The segment table identifies important graph sections. Large positive and negative regions may cancel. Use the listed impulses to verify your area calculations.
Limits and Safe Use
This method assumes a net force along one axis. Include relevant force components. Consider friction, thrust, and gravity components. Do not ignore opposing forces. The tool does not replace vector analysis. It does not model changing mass without separate treatment. Rotational motion requires angular impulse methods. Measured graphs may contain noise. Rounding changes the final digits. More sections improve curved data. Confirm sensor calibration. Show units on every graph axis. Use the impulse value for a check. For design decisions, verify assumptions. Treat the calculation as an analysis aid. It is not a safety certification.
Frequently asked questions
1. What graph is required?
Use a force-time graph. The horizontal axis must represent time. The vertical axis must represent force. Enter each straight section separately.
2. Why does graph area matter?
The signed area under a force-time graph is impulse. Impulse changes momentum. Dividing the momentum change by mass gives velocity change.
3. Can I enter negative forces?
Yes. Negative forces create negative impulse. They reduce positive momentum or increase momentum in the opposite chosen direction.
4. Can initial velocity be negative?
Yes. A negative initial velocity means the object initially moves opposite the positive graph direction. This helps model reversal accurately.
5. Does final speed include direction?
No. Speed is always nonnegative. The calculator also displays signed final velocity and a direction label, which show the motion direction.
6. What does one segment represent?
One segment represents a straight force-time interval. Its force can remain constant or change linearly between the listed endpoints.
7. How should I enter a curved graph?
Split the curve into many short straight intervals. Use measured force values at interval endpoints. More segments usually improve the estimate.
8. What units does the calculator support?
Mass supports kilograms, grams, and pounds-mass. Force supports newtons, kilonewtons, and pound-force. Time supports seconds, milliseconds, and minutes.
9. Why is my final velocity zero?
Your net impulse may exactly cancel initial momentum. Opposing graph areas can also cancel each other. Review signs and starting velocity.
10. Does this calculate distance traveled?
No. Force-time area provides impulse, not distance. Distance needs velocity over time or position information after finding the motion model.
11. Can I use this for engineering decisions?
Use it for estimates and checks. Confirm force directions, units, measurement quality, constraints, and safety requirements before using results in design decisions.