Rate of Change
A student walks 12 meters in 6 seconds in a straight line.
What is the student’s average velocity?
2 m/s
A position–time graph shows a straight line that slopes upward.
What does this tell you about the object’s velocity?
The velocity is positive.
A cart starts from rest and accelerates at 2.0 m/s² for 3.0 seconds.
What is the cart’s final velocity?
6.0 m/s
The change in an object’s position divided by the time.
Velocity
A person starts at their house, walks 5 blocks west, then 3 blocks north, then 5 blocks east, then 1 block south. How many blocks from their house are they? (include direction)
2 blocks north
Car A changes its position from 10 m to 80 m in 10 seconds, while Car B changes its position from 0 m to 90 m in 15 seconds.
Which car has the greater average velocity, and by how much?
Car A has a greater average velocity by 1 m/s.
Go to image 1
2m/s
A ball starts from rest and accelerates at 1.5 m/s² for 4.0 seconds.
How far does it travel in that time?
12.0 m
The rate at which velocity changes over time.
Acceleration
Mr. Hilson leaves his classroom and travels all the way to gym 3, jumps 1 meter into the air (wow!) and then returns to his classroom. What is his displacement?
0 m
A cart’s velocity increases from 2 m/s to 8 m/s in 3 seconds.
What is the cart’s average acceleration?
2 m/s^2
Go to image 2
Line A shows an object moving faster
A car moving at 5.0 m/s accelerates at 3.0 m/s² until it reaches 20 m/s.
How far does the car travel while speeding up?
62.5 m
On a position–time graph, this quantity is represented by the slope of the line.
Velocity
A ball rolls to the right and slows from +6 m/s to +2 m/s in 2 seconds.
What is its average acceleration?
Go to image 3
2.7m/s^2
A car moving in a straight line travels 40 m in 5.0 seconds while accelerating uniformly from rest.
What is the car’s acceleration?
3.2 m/s²
This equation relates final velocity, initial velocity, acceleration, and displacement.
vf^2 = vi^2 + 2ad
An object travels 300 meters north, 200 meters west, and 300 meters south. The entire trip takes 200 seconds. Determine the average speed AND the average velocity (include direction) of this object.
average speed = 4m/s
average velocity = 1m/s west
A car’s velocity changes from –4 m/s to +2 m/s in 3 seconds.
Calculate the average acceleration, and explain what it means that the sign of the initial velocity and the final velocity are different.
2m/s^2, signs are different because the car changes direction.
Go to image 4
moving forward, speeding up
A bike accelerates from 4.0 m/s to 10.0 m/s in 3.0 seconds.
Find the bike’s acceleration and displacement during that time.
a=2.0m/s^2;
d=21.0m
This variable represents how far an object moves in a particular direction, and can be positive or negative.
Constant acceleration OR constant rate of change of velocity