1. A.K.A Cruise Control
Constant Velocity

2. Objectives Understand the difference between speed and velocity
Create and interpret x vs. t graphs
Understand that the slope of the x vs. t graph is the velocity
Derive the equation of motion for constant velocity from a graph of x vs. t
Use the constant velocity equation to solve problems

3. Speed and Velocity Speed – distance traveled over time
Speed is a scalar – magnitude only; just a number and units
the number on your speedometer
how fast you’re going
Velocity – The change in position over time.
Velocity is a vector – magnitude + direction; a number with units and orientation
the number on your speedometer + the letter on your compass
how fast you’re going + the direction of travel
Sign convention: + means away from the origin, - means toward the origin
𝑠= 𝑑 𝑡

4. Vectors have magnitude and direction. Scalars only have magnitude.
𝑠𝑝𝑒𝑒𝑑= 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦=𝑠𝑝𝑒𝑒𝑑+𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
Vectors have magnitude and direction. Scalars only have magnitude.

5. Distance and Displacement
Distance (d) is a scalar – the amount of ground covered
The distance between school and your house
A number – nothing else; your odometer reading
20 miles
Displacement (Δx) is a vector – the change in position
The displacement from school to your house
Direction included
20 miles southwest
Final position – initial position

6. Create and interpret x vs. t graphs
Y-intercept = initial position
Slope = velocity

7. The Significance of the Slope
The slope of a line is given by 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = ∆𝑦 ∆𝑥
In our case x = t and y = x, so the slope of our line is ∆𝑥 ∆𝑡 .
Velocity is defined as the change in position over time, therefore, 𝑣= ∆𝑥 ∆𝑡 .
The slope of any position vs. time graph is the velocity.

8. Derive the equation of motion for constant velocity from a graph of x vs. t
Our equation for velocity is 𝑣= ∆𝑥 ∆𝑡 .
Multiplying by Δt, we get 𝑣×∆𝑡= ∆𝑥
You may have seen this before in math as
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑟𝑎𝑡𝑒 × 𝑡𝑖𝑚𝑒
The symbol delta Δ means change, but more specifically final – initial conditions, therefore, ∆𝑥= 𝑥 𝑓𝑖𝑛𝑎𝑙 − 𝑥 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝑥 𝑓 − 𝑥 0
Plugging this into our velocity equation gives us 𝑣×∆𝑡= 𝑥 𝑓 − 𝑥 0 which simplifies to 𝑥 𝑓 =𝑣∆𝑡+ 𝑥 0
If this looks a lot like the general equation of a line (𝑦=𝑚𝑥+𝑏) to you, good. It is.

9. Summary Create a circle map for constant velocity Constant Velocity
Equations
Examples
Concepts
Definitions
IRL
Graphs

10. Use the constant velocity equation to solve problems
A car is travelling down the road at 20 m/s. How far has the car gone after 30 seconds?
One time around the track is 400m, if a runner can complete her race in 70 seconds, what is her average speed?
A buggy begins at 30 cm and moves to 60 cm in two seconds. What is the velocity of the buggy? What is the speed of the buggy?
The buggy is now turned around and moves from 90 cm to 30 cm in 4 seconds. What is the velocity of the buggy? What is the speed of the buggy?