QQ: Show Work! Jonathon runs 4.0 km in 32 minutes, then 2.0 km in 22 minutes, and finally 1.0 km in 16 minutes. What is his average speed in km per minute? A train travels 190 km in 3 hours and then 120 km in 2 hours. What is its average speed? Jose drove 85 km from Town A to Town B, then 45 km Town B to Town C. The trip took 1.5 hours. What was the average speed?
Today’s objective: I can calculate average speed, velocity, and acceleration using data, examples, and graphs.
Speed, velocity, and acceleration… are they basically the same thing?
What’s happening here? Frame of reference video hyperlink
Is it possible to slide a pencil through both of these frames at the same time?
Frame of Reference: The point which movement is measured from considering the objects around it.
Speed: The average rate of travel in a given period of time. Usually written in relation to 1 period of time for example: 16 mph or 3 m/s 10 feet/min
The exact speed a vehicle is traveling at a specific time. Instantaneous Speed: The exact speed a vehicle is traveling at a specific time.
Hayle & Yesenia went to the beach during break. They left MHS at noon Hayle & Yesenia went to the beach during break. They left MHS at noon. After driving 124 km they stopped in Wilmington to eat at 1:30pm. They got back on the road at 2:30 and drove 120 km. They got to their hotel at 4:00pm. What was the average speed they traveled?
What factors affect the average speed? Does that mean that every time they looked at the speedometer is showed that speed? What factors affect the average speed?
The slope is the average speed Graph of speed: The slope is the average speed position time
Average speed: 8 – 4 4 2 = 2 m/s 4 - 2
Because it has the steepest slope Which has the highest average speed? Because it has the steepest slope
This is a graph of Luis on his motorcycle. Describe his movement here:
Dylan’s parents put a gps devise in his car Dylan’s parents put a gps devise in his car. Where is he not moving at all?
Where is he moving the fastest?
Where is he moving the slowest?
Vector: Shows direction and magnitude.
Velocity: Describes both Speed AND direction VECTOR
Velocity: V = velocity D = distance T = time
Rate that velocity changes over time What is Acceleration? Rate that velocity changes over time Vf final velocity Vi initial velocity T is time
m/h/s m/s/s m/s2 Acceleration: Changes in speed, direction, or both Unit of measurement: m/h/s m/s/s m/s2 Vector
Constant Acceleration Linear: straight line – no changes in speed Velocity time Linear: straight line – no changes in speed
Increasing acceleration: Greater slope = faster acceleration
Negative Acceleration Deceleration: Slowing down or a negative slope Negative Slope Also known as Negative Acceleration
A ball rolls down a ramp, starting from rest A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 m/s. What is the acceleration of the ball? 6 m/s 0 m/s 2s M/s2
Draw a dot at the intersection of 2 lines near the bottom edge of the graph paper on your desk. Label it “Start.” Draw a 2nd dot near the top of the paper. Label it “End.” Draw a path from the start to the stop point. Any route is ok as long as it doesn’t go off the grid lines 4. Determine the total length of your path. Each segment is 1 cm.
Vector addition & subtraction: Add the values together 3m/s 5 m/s 8 m/s Same direction: Add the values together
Add like negative numbers 5m/s 2 m/s 3 m/s Opposite directions: Add like negative numbers
Distance: The length of the path between two points.
SI unit: Meter Football Field: 91.4 m
Length of Mississippi: 1000 m = 1 km Or 3780 km
Distance a marble can roll 1m = 100 cm Or 6 cm
Back to the graph…
The straight line drawn Displacement: The straight line drawn between 2 points.
Observing: Which is the shorter distance, your first path or the second one? End Start
Evaluating and Revising: your original distance shorter? End Start Evaluating and Revising: How could you have made your original distance shorter?
End Start Inferring: If you keep the start and end points the same, would it be possible to make the displacement shorter?
starting point to the ending point Displacement: The distance from the starting point to the ending point
Vector addition & subtraction: Determines displacement 8km 5km 8km + 5km = 13km
Vector addition & subtraction: Determines displacement 9km 14km 5km 14km -5km = 9km
Resultant Vector: The result of adding two vectors
1. Find the speed of the green bus at 1 hour. Use the graph below to answer the questions. Be sure to show all work. 1. Find the speed of the green bus at 1 hour. 2. Find the speed of the red bus at 3 hours. 3. How far will the green bus travel in 8 hours?