Position Time Graph Answers- Complete Analysis Guide
What Is a Position Time Graph?
A position time graph shows how an object's location changes over a period of time. The x-axis represents time, while the y-axis represents position relative to a reference point.
This is one of the most fundamental graphs in physics. It tells you where something is at any given moment and lets you calculate how fast it's moving.
If you're looking for quick answers to specific problems, skip ahead. But if you actually want to understand what the graph is showing you, read the whole thing.
How to Read a Position Time Graph
The slope of the line tells you velocity. Steeper slope means faster motion. Negative slope means the object is moving backward toward the reference point.
Straight Lines vs. Curved Lines
A straight line means constant velocity. The object covers equal distances in equal time intervals.
A curved line means changing velocity — the object is accelerating or decelerating. You need calculus to find the exact velocity at any point on a curve.
Horizontal Lines
A horizontal line means the object is not moving at all. Position stays the same while time passes.
Calculating Velocity from a Position Time Graph
For straight lines, the velocity is simply the slope. Pick two points on the line and use:
Velocity = (Change in Position) ÷ (Change in Time)
Example: An object moves from x = 10m to x = 30m in 4 seconds.
Velocity = (30 - 10) ÷ (4 - 0) = 20 ÷ 4 = 5 m/s
That's it. No fancy formulas needed for linear motion.
Common Position Time Graph Shapes and What They Mean
- Upward sloping straight line — moving away from origin at constant speed
- Downward sloping straight line — moving toward origin at constant speed
- Horizontal line — standing still
- Curved line curving upward — speeding up (positive acceleration)
- Curved line curving downward — slowing down
- Vertical line — physically impossible in real motion
Sample Problems and Answers
Problem 1
An object starts at position 0m. After 5 seconds, it's at 20m. What is its average velocity?
Answer: 20m ÷ 5s = 4 m/s
Problem 2
A graph shows a line from (0s, 0m) to (3s, 15m) to (6s, 15m). Describe the motion.
Answer: The object moves away from origin at constant velocity for 3 seconds, then stops. During the first 3 seconds, velocity = 15m ÷ 3s = 5 m/s. After 3 seconds, velocity = 0.
Problem 3
Which object is moving faster: one with a slope of 2 m/s or one with a slope of -5 m/s?
Answer: It depends what you mean by "faster." If you mean speed (how fast, regardless of direction), the second object is faster at 5 m/s. If you're comparing velocity values, they're different directions, not magnitudes.
Comparing Motion Analysis Methods
| Method | Best For | Difficulty |
|---|---|---|
| Position Time Graph | Visualizing overall motion | Easy |
| Velocity Time Graph | Finding acceleration | Medium |
| Equations of Motion | Precise calculations | Medium |
How to Draw a Position Time Graph
Follow these steps:
- Label your axes. Time goes on x-axis, position on y-axis.
- Choose appropriate scales. Don't cram everything into a tiny corner.
- Plot your data points accurately.
- Connect the points. Use straight lines for constant velocity, curves for changing velocity.
- Add units to your labels. "Time (s)" and "Position (m)" not just "time" and "position."
Getting Started: Quick Reference
When you see a position time graph question:
- Look at the slope direction. Positive? Negative? Zero?
- Is the line straight or curved?
- Calculate slope if it's straight.
- Identify key points — where does motion start, stop, or change direction?
Most exam questions test these basics. Master slope calculations first, then worry about curves.
Common Mistakes Students Make
Confusing position with displacement. Position is where you are. Displacement is how far you've moved from start. On a graph, displacement is total change in position, not total distance traveled.
Forgetting that negative slope still has a real velocity. Objects moving in the negative direction have negative velocity. That's not "no motion."
Treating curves like straight lines. You can't just pick two points on a parabola and call it constant velocity. The slope changes at every point.