Speed & Velocity Measuring Motion

AGENDA Bell Work Notes on Speed Hot Wheelin’ Speed Lab Exit Pass HW Collected Notes on Speed Hot Wheelin’ Speed Lab Exit Pass Homework Announcements

Bell Work Imagine cars driving on a freeway, how would you describe their movement? Use as many details or description as you can. What are some examples?

OBJECTIVES: Relate speed to distance and time. Standard 3.2: Explain and describe what is acceleration. Write the equation (formula) for speed. Solve problems using the equation for speed. Relate speed to distance and time. Solve problems using speed, time, and distance. Create distance-time graphs. Create speed-time graphs.

S = d/t Calculating Speed: Speed (S) = distance traveled (d) ÷ the amount of time it took (t). S = d/t

Manipulating the Speed Formula: What if you wanted to find out speed (HOW FAST)? D Since D is above the T, we know we have to divide OR S T D T

Manipulating the Speed Formula: What if you wanted to find out the distance (HOW FAR)? D Since S is next to the T, we know we have to multiply OR S T S X T

Manipulating the Speed Formula: What if you wanted to find out the time (HOW LONG)? D HOW LONG – does not mean how far… DO NOT FORGET! Since D is above the S, we know we have to divide OR S T D S

Don’t Forget About Your Units: meters (m) meters per second OR m/s S T seconds (s)

S = d/t Calculating speed If I travel 100 kilometer in 2 hours then I have a speed of… 100÷2 = 50 km/h If my speed is 50 m/s in 5 seconds then I have a distance of…. 50 X 5 = 250 m

Velocity Velocity – the SPEED and DIRECTION of an object. Example: An airplane moving North at 500 mph A missile moving towards you at 200 m/s

Question What is the difference between speed and velocity? Speed is just distance/time. Velocity includes direction as well. Speed is just distance/time. Velocity includes direction as well.

Graphing Speed: Distance vs. Time Graphs Denver Phoenix

Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/Run Rise

Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/Run Rise=? 600 km 3 h

Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/Run Rise=? 600 m 3 minutes Rise/Run = 600 km/3 hr = 200 km/hr

Different Slopes Slope = Rise/Run = 0 km/1 hr = 0 km/hr Rise = 2 km Run = 1 hr Rise = 0 km Run = 1 hr Slope = Rise/Run = 2 km/1 hr = 2 km/hr Rise = 1 km Run = 1 hr Slope = Rise/Run = 1 km/1 hr = 1 km/hr

Average Speed = Total distance/Total time = 12 km/6 hr Question Below is a distance vs. time graph of my position during a race. What was my AVERAGE speed for the entire race? Average Speed = Total distance/Total time = 12 km/6 hr = 2 km/hr Rise = 12 km Run = 6 hr

Question What does the slope of a distance vs. time graph show you about the motion of an object? It tells you the SPEED

Question Below is a distance vs. time graph for 3 runners. Who is the fastest? Leroy is the fastest. He completed the race in 3 hours

Speed-time graphs 1) Speeding Up 4) Slowing down 80 60 40 20 4) Slowing down Speed m/s 3) Speeding up, slower than first increase (slope is less steep) 2) Same (constant) Speed T/s 10 20 30 40 50

Distance-Time (Position) Graphs 1) Constant Speed 80 60 40 20 4) Going back, but at constant speed Distance (m) 3) Speeding up, but slower 2) Stopped T/s 10 20 30 40 50

Acceleration Acceleration = speeding up How much faster or how much slower you are going with a direction Acceleration – the rate at which velocity changes Can be an: Increase in speed Decrease in speed Change in direction DECELERATION

Types of acceleration Increasing speed Decreasing speed Example: Car speeds up at green light Decreasing speed Example: Car slows down at stop light Changing Direction Example: Car takes turn (can be at constant speed) screeeeech DECELERATION

Question How can a car be accelerating if its speed is a constant 65 km/h? If it is changing directions it is accelerating

Calculating Acceleration If an object is moving in a straight line Final Velocity – Initial Velocity ACCELERATION = Time A = Vf-Vi t Units of acceleration: m/s2 or m/s/s m/h/h or m/h2

Calculating Acceleration 0 s 1 s 2 s 3 s 4 s 0 m/s 4 m/s 8 m/s 12 m/s 16 m/s

Question A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver’s average acceleration?

Acceleration – What is it exactly? Time (s) Speed (m/s) 1 2 3 4 5 6 7 8 What is happening to your speed if you have an acceleration of 5 m/s2? 5 10 15

Acceleration – What is it exactly? Time (s) Speed (m/s) 1 2 3 4 5 6 7 8 What is happening to your speed if your speed is 20 m/s but have an acceleration of 10 m/s2? 20 10 -10 -20 -30 Are you slowing down? No, you’re just going the other way.

Acceleration Graphs 1) Increasing acceleration (speed getting faster by certain amount each second) 80 60 40 20 4) Deceleration Acceleration m/s/s 3) Increasing acceleration 2) Constant Acceleration (speed is still increasing) T/s 10 20 30 40 50

Acceleration – What is it exactly? What if we know the acceleration, how do we find the final speed, the start speed, or even how long it took (time)? t = Vf - Vi How long? (Time) a Vf= at + Vi Final Speed (Vf) Vi= Vf - at Initial Speed (Vi)

Now your turn: Try a couple of these problems: a = Vf - Vi Acceleration t t = Vf - Vi How long? (Time) a Vf= at + Vi Final Speed (Vf) Vi= Vf - at Initial Speed (Vi)