Which graph has the greater velocity? The greater acceleration? Objective: I will be able to describe position, velocity and acceleration mathematically Bellringer Which graph has the greater velocity? The greater acceleration?

Today: Describing position, velocity and acceleration mathematically. Due today: Science fair Procedure and Materials.

Velocity as Slope How far does the baseball travel in 20 s?

Velocity as Slope Which has the largest velocity?

P vs T: Toy Boat Find velocity on each interval:

P vs T: Toy Boat

P vs. T: Hawk Find Velocity on each interval, then sketch V vs. T

P vs. T: Hawk

V vs. T sketching A man fills his wheelbarrow with mulch then slowly rolls it to his garden at a constant velocity. He stops to unload the wheelbarrow, then rolls it back to the mulch pile at a constant velocity. On his way back, his wheelbarrow is much lighter so he travels twice as quickly.

V vs. T Sketching

V vs. T sketching Cordell runs from the school to Jim’s to get a hot dog. He slows down just before he gets to the road, then stops to make sure no cars are coming. He speeds back up as he crosses the road then stops at the door to Jim’s.

V vs. T sketching

Bellringer Which shows an object speeding up? Slowing down? Going at a constant, fast speed? Constant, slow speed?

Velocity is Slope… So we can use it to write Position vs. Time in slope intercept form: y = mx +b d = vt + d0

Velocity is Slope… Graph: y = 2x - 3 d = -2t + 1

Velocity is Slope… d = -2t + 1 What is the initial position of the object? What is the velocity?

Velocity is Slope… Mia is 2 miles South of her house. She begins running toward her house at a velocity of 4 miles/hour. Write an equation to represent Mia’s position.

Velocity is Slope… Mia is 2 miles South of her house. She begins running toward her house at a velocity of 4 miles/hour. d = 4t - 2

Velocity is Slope… Breyanna races home from school to watch her favorite cartoon. She starts out 6 km North of her house and runs at a rate of 1 km/min. Write an equation to represent Breyanna’s position.

Velocity is Slope… Jquan wants to check some books out of the library to learn how to care for his pet hippopotamus. He starts out 3 km East of the library and walks 2 kilometers every 3 minutes What is the equation for Jquan’s position?

Acceleration is slope! We can describe velocity using a slope intercept equation. Our variables will be v, vo, t and a. What do you think the equation will look like?

Acceleration is slope! v = at + vo

Acceleration is slope! With a partner: Write a situation with an initial velocity and an acceleration, then write an equation, then plot it on a velocity vs. time graph.

Revisiting “Average” Remember: these are averages over an interval.

Revisiting “Average” “From 0-1 s, the average v is 1 m/s”

Revisiting “Average”

Revisiting “Average” We can treat acceleration the same way