1. Speed & Velocity

2. Speed = Distance / Time Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∆ 𝑇𝑖𝑚𝑒
∆ (“delta”) means “change in…”
division sign means “per…”
Units: miles per hour (mph) meters per second (m/s) kilometers per hour (km/hr)

3. 5 meters in 1 second: 10 meters in 2 seconds: 20 meters in 10 seconds:
Biking Speeds:
5 meters in 1 second:
5 m/sec
10 meters in 2 seconds:
20 meters in 10 seconds:
2 m/sec

4. Velocity: Speed with direction
Biking at 2 m/sec to the north
Flying at 120 mph to the SW

5. Velocity: Speed with direction
An airplane travels 250 km due north in 1/2 hour.
Speed?
500 km/hr
Velocity?
500 km/hr north

6. Vocabulary: Vector vs. Scalar
Has a size (magnitude) AND a direction
Example – Velocity
Scalar:
Has a size (magnitude)
Example - Speed

7. Displacement: Distance with direction
Distance – How FAR an object has traveled
Driving to Spokane – and back
Running around the classroom
Scoring a soccer goal
SCALAR quantity (size only, no direction)
Displacement: How much the position has changed (Takes “direction” into account. A VECTOR quantity)
VECTOR quantity (size AND directi0n)

8. Displacement: Distance with direction
Distance – How FAR an object has traveled
Driving to Spokane – and back
Running around the classroom
Scoring a soccer goal
SCALAR quantity (size only, no direction)
Displacement: How much the position has changed (Takes “direction” into account. A VECTOR quantity)
VECTOR quantity (size AND directi0n)

9. Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 ∆ 𝑇𝑖𝑚𝑒 = 𝑑 ∆ 𝑡
Velocity = ∆ 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 ∆ 𝑇𝑖𝑚𝑒 = ∆ 𝑥 ∆ 𝑡

10. Velocity: Slope of position vs. time graph
𝑠𝑙𝑜𝑝𝑒= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑚 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒 (𝑠𝑒𝑐) = ∆ 𝑥 ∆ 𝑡 = 50 𝑚 −0 𝑚 5 sec − 0 𝑠𝑒𝑐 = 10 m/s

12. Instantaneous vs. Average
Speedometer: Shows speed at this instant => Instantaneous speed
Calculate: 𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡𝑟𝑖𝑝 𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 => Average speed

13. Instantaneous vs. Average
Drive to Seattle
Instantaneous speeds:
31 mph on Cemetery Road
18 mph slowing down for a traffic light
57 mph on I-405
42 mph on I-90
Average speed:
20 miles in ½ hour = 40 mph