Enter Velocity Segments
Use one to five constant-velocity segments. Negative velocity moves position downward.
Example Data Table
| Segment | Velocity | Time | Position Change | Ending Position |
|---|---|---|---|---|
| 1 | 6 m/s | 5 s | 30 m | 30 m |
| 2 | 2 m/s | 4 s | 8 m | 38 m |
| 3 | -3 m/s | 3 s | -9 m | 29 m |
The graph rises quickly, rises slowly, then falls. Each straight line section has a slope equal to the entered velocity.
Formula Used
For each constant-velocity segment, the calculator uses Δx = v × Δt. Here, Δx is position change, v is velocity, and Δt is the duration.
It then adds each segment change to the earlier position: xfinal = xinitial + Σ(vi × Δti). The slope of every straight graph section equals that segment velocity.
Average velocity uses net displacement: vavg = (xfinal − xinitial) / total time. Distance travelled adds the absolute size of every segment change.
How to Use This Calculator
- Enter the starting position in your selected distance unit.
- Choose one distance unit and one time unit.
- Add velocity and duration for each motion segment.
- Use negative velocity when the object travels backward.
- Select Create Position Graph to calculate all positions.
- Review the graph, totals, segment table, and export choices.
Understanding Velocity and Position Over Time
A velocity to position time graph turns motion information into a location record. Velocity tells how quickly position changes. Position tells where the object is at a given time. The calculator connects those ideas through repeated, simple steps.
Start with a known position. Then multiply each constant velocity by its duration. That product is the displacement for one segment. Add the displacement to the previous position. Repeat this process until every segment is complete.
On the finished graph, time runs horizontally. Position runs vertically. A rising line means positive velocity. A falling line means negative velocity. A horizontal line means zero velocity. The steepness of the line shows the size of velocity.
Why Segments Matter
Real trips often change speed. A cyclist may start quickly, slow near a crossing, and reverse direction. One average number can hide those changes. Segments preserve the movement pattern. They let the graph display each motion stage clearly.
Use one segment for steady motion. Use several segments for changes in speed or direction. You may also use a zero velocity segment. It creates a flat position line. That means the object remained at the same location during that period.
Reading the Shape
A position graph does not show speed directly on the vertical axis. Instead, it shows location. Velocity appears in the slope. A steeper upward slope represents a larger positive velocity. A steeper downward slope represents a larger negative velocity.
Two lines can end at the same position but describe different trips. One object may travel forward and then backward. Another may move slowly in one direction. The final position matches, yet the total distance can differ. This calculator reports both values.
Using Consistent Units
Keep units consistent inside every calculation. When distance uses metres and time uses seconds, velocity must use metres per second. When distance uses miles and time uses hours, velocity must use miles per hour. Mixed units produce misleading graph points.
Choose an initial position carefully. It shifts the whole graph upward or downward. It does not change slopes. This separation is useful when comparing two objects that move identically but begin at different locations.
Checking Your Result
Review each segment table row before trusting the final result. Check the velocity sign. Check the duration. Check the ending position. A backward trip should reduce position. A pause should keep position unchanged. These simple checks catch many input mistakes.
Graphs also show when an object crosses the origin. Find the time where its position becomes zero. Interpolate only when a line segment crosses that level. This detail helps compare motion, identify returns, and explain movement through clear graphical reasoning for classwork. It also strengthens visual reasoning before solving more complex motion questions later.
The exported CSV supports homework checks, lab notes, and spreadsheet analysis. The graph image supports reports and presentations. Use the print option when a paper copy or saved PDF is useful. Clear graph results support better motion decisions every day.
Frequently Asked Questions
1. What does this calculator create?
It calculates position values from constant-velocity segments and draws a position-versus-time graph. It also reports total time, displacement, distance travelled, and average velocity.
2. Can I enter negative velocity?
Yes. Negative velocity moves the position downward over time. It is useful for return trips, reverse motion, or movement opposite to the chosen positive direction.
3. What does a flat graph section mean?
A flat section means the position did not change. Enter a velocity of zero for that segment. The object remains at rest during the entered duration.
4. Why is position different from distance travelled?
Position describes location relative to the chosen origin. Distance travelled counts every movement length. A return trip can have a large distance but a small final displacement.
5. What is the slope of a position-time graph?
The slope equals velocity. An upward slope is positive velocity. A downward slope is negative velocity. A steeper line means a larger velocity magnitude.
6. How many motion segments can I use?
This page accepts up to five segments. Leave unused segment fields blank. At least one complete velocity and duration pair is required.
7. Can velocity change inside one segment?
No. Each segment assumes constant velocity. Split changing motion into shorter segments whenever velocity changes. This keeps the position graph accurate for the entered data.
8. Which units should I choose?
Choose one distance unit and one time unit. Then enter velocity using those same units per time. For example, use metres and seconds with metres per second.
9. How is average velocity calculated?
Average velocity equals total displacement divided by total time. It uses the starting and final positions. It does not equal average speed when direction changes.
10. Can I download the results?
Yes. After calculation, download the segment data as CSV, save the graph as a PNG image, or use the print option to save a PDF.
11. Does the starting position affect the graph?
Yes. It moves every graph point up or down by the same amount. It does not change the velocity slopes or segment displacement values.