1. (D-T Graphs, sometimes called P-T or Position-Time Graphs)
Distance-Time Graphs
(D-T Graphs, sometimes called P-T or Position-Time Graphs)

2. The Meaning of Shape for a d-t Graph
We can use distance vs. time graphs to describe motion. The motion of an object is reflected in the shape and the slope of the lines on a distance vs. time graph.

3. A car moving right…
To begin, consider a car moving with a constant, rightward (+) velocity - of +10 m/s.

4. Distance-time graph
This is the distance-time graph for this car. Note that a motion described as a constant, positive velocity results in a line of constant and positive slope when plotted as a position-time graph.

5. Distance-time graph
Now consider a car moving with a rightward (+), changing velocity - that is, a car that is moving to the right but speeding up or accelerating.

6. Distance-time graph
The resulting graph would look like this. Note that a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph.

7. The Importance of Slope
Rightward direction
Positive Velocity Changing Velocity (acceleration)
Rightward direction
Positive Velocity
Constant Velocity

8. The Importance of Slope Slower velocity/speed Faster velocity/speed
The faster the speed, the steeper the slope.

9. Leftward Velocity
Slow, Leftward(-) Fast, Leftward(-) Constant Velocity Constant Velocity

10. Leftward velocity Leftward(-) Velocity Slow to Fast
Leftward (-) Velocity Fast to Slow

11. ZERO slope on a D-T graph means the car is STOPPED
Think – the distance doesn’t change as time goes by. This
means the car is standing still.

12. In Summary:
The shape of the line on the graph (straight, curving, steeply sloped, mildly sloped, etc.) is descriptive of the object's motion.
A zero slope means the car is stopped
A shallow slope means a slow speed;
A steep slope means a fast speed;
A positive slope means going in a certain direction;
A negative slope means going in the opposite direction;
A constant slope (straight line) means a constant speed;
A changing slope (curved line) means a changing speed
(acceleration).