1. Instantaneous position – the position at a particular instant.
2.3 Position-Time Graphs
Draw a position-time graph of two brothers running a 100 m run. The younger brother started the race from the 20 m mark. The older brother passed the younger brother at 6 seconds, at the 60 m mark. Both brothers run at a constant speed.
Instantaneous position – the position at a particular instant.

2. 2.4 How Fast?

3. 2.4 How Fast?

4. 2.4 How Fast?

5. 2.4 How Fast?
The jogger in red is moving faster because she has a greater displacement, Δd, during a fixed time interval

6. 2.4 How Fast?

7. 2.4 How Fast?
It is a common misconception to say that the slope of a position-time graph gives the speed of the object.
The slope of a position-time graph for an object is the object’s average velocity - the change in position (displacement) divided by the time during which the change occurred.
indicates an average

8. What is the slope of this line? -5.0 m/s
2.4 How Fast?
What is the slope of this line?
-5.0 m/s
The slope indicates BOTH magnitude AND direction (velocity is a vector!!)

9. The sign of the slope tells the direction the object is moving
2.4 How Fast?
slope = -5.0 m/s
The absolute value of the slope (5.0 m/s) is the average speed – how fast the object is moving
The sign of the slope tells the direction the object is moving
Speed is the magnitude of a velocity vector

10. 2.4 How Fast?
instantaneous velocity – the speed and direction of an object at a particular instant (the line tangent to a single point).

11. Position-time graph for an ostrich
2.4 How Fast?
Position-time graph for an ostrich
What was the speed of the ostrich between t = 30 s and t = 40 s?

12. Position-time graph for an ostrich
2.4 How Fast?
Position-time graph for an ostrich
What was the velocity of the ostrich between t = 40 s and t = 80 s?

13. Particle model depicting the velocity of two objects
2.4 How Fast?
Particle model depicting the velocity of two objects
Which object is traveling faster?
How do you know?

14. What is the average velocity for the total trip?
2.4 How Fast? Ex
A bus traveled south along a straight path for 2.0 hours with an average velocity of 54 km/hr, stopped for 15.0 minutes, then traveled south for 1.5 hours with an average velocity of 60 km/hr.
What is the average velocity for the total trip?
What is the displacement for the total trip? Ex
A child can push a shopping cart at a speed of 1.2 m/s. How long would it take this child to push the cart down an aisle with a length of 11.0 m?