1. SCI 10 Physics
Speed and Velocity

2. Slopes on distance- time graphs tell us: average SPEED
Slopes on position-time graphs tell us: average VELOCITY

3. Review

4. Speed = distance ÷ time v = d ÷ t
Speed: describes how fast something is moving. It is a scalar quantity (does NOT indicate direction)

5. Practice Question
A bird is observed to fly 50 meters in 7.5 seconds. Calculate the speed of the bird in m/sec.
You are asked for speed in m/s.
You are given distance = 50 m; time = 7.5 s
Use v = d ÷ t
Plug in values and solve. v = 50 m ÷ 7.5 s ≈ m/s

6. Example:
High speed elevators (like the ones in the CN Tower in Toronto), can attain a speed of 7.11m/s.
From questions like this we can calculate the answer to other questions such as…
How much time would the CN tower elevator take to climb 37.5m (about 10 stories)?

7. Manipulating the Equation
Speed = distance ÷ time Distance = speed x time Time = distance ÷ speed Equation Triangle: d v t

8. Average vs. Instantaneous Speed
As an object moves, it often undergoes changes in speed.
Example:
During an average trip to school, there are many changes in speed. Rather than the speedometer maintaining a steady reading, the needle constantly moves up and down to reflect the stopping and starting and the accelerating and decelerating.

9. Average vs. instantaneous speed
Average speed is the total distance traveled divided by the total time taken.
Instantaneous speed is the apparent speed at any moment, such as on a speedometer.

10. One instant, the car may be moving at 50 km/hr and another instant, it might be stopped (i.e., 0 km/hr). Yet during the course of the trip to school the person might average 25 km/hr.
The average speed during the course of a motion is often computed using the following equation:
Average speed = total distance traveled
total time
Vav = ∆d ∆t

11. Since a moving object often changes its speed during its motion, it is common to tell the difference between the average speed and the instantaneous speed.
Instantaneous Speed - speed at any given instant in time. (vinst)
Average Speed - average of all instantaneous speeds; found simply by a distance/time ratio. (vavg)

12. Try These:
a) How far does a car travel if it moves at a speed of 50 km/h for 4.5 hours?
b) How long does it take a rabbit to hop 500m if he can travel at an average speed of 4 m/s?
c) How fast does a cyclist need to go in order to complete 12 km in 30 minutes?
(record your answer in km/h)

13. Velocity: Speed with Direction
Velocity is a vector quantity which refers to "the rate at which an object changes its position."
Velocity = displacement
time
v = ∆d t

14. The Equation Triangle Δd v t
The triangle for velocity is the same for speed with one minor difference
We use displacement instead of distance and therefore there are vectors involved! Δd v t

15. Velocity
Because velocity is a vector it can be positive, negative or zero. Example: A hiker has travelled 5km North in 2 hours. Calculate the average velocity. Velocity = 5 km, North 2hrs = 2.5 km/h North

16. The slope of a position-time graph is the velocity!
The slope will show the change in displacement over the amount of time it took to travel

17. Two cars going opposite directions have the same speed, but their velocities are different—one is positive and the other is negative.

18. Velocity Examples:
The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average velocity.
Remember that the displacement refers to the change in position and the velocity is based upon this position change.
In this case of the teacher's motion, there is a position change of 0 meters and therefore an average velocity of 0 m/s.

19. Speed vs. velocity Ysain Bolt

20. How far do you go if you drive for 2 h at a speed of 100 km/h?
Solving Problems
How far do you go if you drive for 2 h at a speed of 100 km/h?
Asked for? Distance
Know/given: time = 2 h, v = 100 km/h.
Use d = vt.
Solve. d = 2 h × 100 km/h = 200 km

21. What is her average velocity (in m/s) once she reaches B? C? and D?
Example Problem
750m m 600m
C A B D
A cross country skier starts at position A and skies to B in 5 minutes. She turns and arrives at C by 12 minutes and then turns again and skies to D where she stops at 20 minutes.
What is her average velocity (in m/s) once she reaches B? C? and D?