First seating chart

Warm UP Imagine dropping two rocks from rest, one after the other. When the first rock has fallen 4m, you drop the second rock. As the two rocks continue their free fall, does their separation increase, decrease or stay the same? Defend your answer

answer At any given time, the first rock has a greater velocity than the second rock, therefore the first rock will always be increasing its lead as it falls

Galileo Galilei ( 1564- 1642)

Falling elephant and feather

Free fall in a vacuum (no air resistance)

What did Galileo conclude about objects in free fall? Galileo concluded that if the effects of air resistance can be neglected, then all object in free fall have the same constant acceleration.

Each second of instantaneous velocity of the object increases by additional 9.81 m/s For quick calculation use 10 meter per second Acceleration = (10 m/s)/ 1 s = 10m/s2 Velocity (v )  m/s Time ( t ) s Acceleration ( a ) m/s2

Free falling objects are always acceleration Free fall happens even when the person is moving upwards. Acceleration is the same at all time while the person is in the air.

Acceleration Due to Gravity ( g ) Gravity at the Earth’s surface  g Magnitude of g = 9.81m/s2 ag = acceleration due to gravity (downward towards center of the earth) ; down = negative ag = g = - 9.81 m/s2 *** gravity (g) is an acceleration, downward towards the center of the earth.

What is the velocity at the top? What is the acceleration at the top?

Velocity time graph The slope of the line = to the ball’s acceleration. What is the ball’s acceleration?

Velocity time graph 1) When is the velocity zero? 2) When does the ball have maximum velocity?

1) What does the slope of the curve on the position-time graph represents? 2) What does the slope of velocity-time graph represent?

Free Fall : for simplicity for simplicity using g = 10 m/s2 What is the difference between instantaneous speed and average speed? After 1 second the object has velocity of 10 m/s ; does this mean the object fell 10 m? Elapse time Seconds ( s ) Instantaneous speed Meter/second m/s 1 10 2 20 3 30 4 40 5 50 - t 10 t

Average speed : How to find average velocity: Velocity starts at 0 and it took 1 second to reach 10 m/s ; therefore the average velocity is between 0 and 10m/s How do you find the average of any two numbers? Find the average of the numbers 3 and 7

Instantaneous velocity Free Fall During the span of the second time interval, the object begins at 10m/s and ends at 20m/s. What is the average velocity of the object during this 1-second interval? What is its acceleration? Elapse time Seconds ( s ) Instantaneous velocity Meter/second m/s 1 10 2 20 3 30 4 40 5 50 - t 10t

Free fall distance of an object dropped from rest To make arithmetic easier use g = 10 m/s2 An apple drops from a tree an hits the ground in one second. 1) What is its average velocity upon hitting the ground ? 2) How high above ground was the apple when it first dropped? Δy= distance in the y direction meaured in meters Elapse time ( t ) in seconds (s) Distance fallen in Δy meters (m) 1 5 2 20 3 45 4 80 125 - t Δy=½ gt2

Calculate height A stone is dropped down a well and it takes 1.6 seconds to reach the bottom. How deep is the well? You may assume the initial speed of the stone is zero. Given: t = 1.6 s vi = 0 m/s  a = 9.81 m/s2 Unknown= Δy= distance Δy = 1/2gt2 y = (0.5)(-9.8 m/s2)=12.5 m 1) You are asked for distance. 2) You are given an initial speed and time of flight. 3) v = vo - gt y = yo + vot - 1/2gt2 4) Since yo = vo = 0, the height equation reduces to: y = - 1/2gt2 y = - (0.5)(9.8 m/sec2) × (1.6 sec)2 y = -12.5 meters The negative sign indicates the height is lower than the initial height by 12.5 m.

Take your HW out – it will be stamp for completion and collected at the end Warm up 1) Speed is the rate at which what happens? Distance changes over time 2) Does the speedometer of the car read read instantaneous speed or average speed? Instantaneous speed 3) What controls on a car cause a change in speed? What controls on a car causes change in velocity only? Acceleration and brake pedal, velocity only steering wheel 4) Acceleration is rate at which what happens? Velocity changes 5) What is the acceleration of the car that travels in a straight line at a constant speed of 100km/h? Zero, there is no change in velocyti 6)Why does the unit of time enter twice in the unit of accelerations? Once for speed change, and again for time change ( m/s2)

Quiz return 1) How is the average velocity calculated when the acceleration is constant? Version A 2) A motor scooter is stopped at a traffic light. When the light turns green, the scooter accelerates at 4.2 m/s2 . A) What is the velocity of the scooter after 3.0 seconds? B)How far does the scooter travel in this time? Version B 2)A boat moves slowly inside a marina with a constant speed of 1.50 m/s. As soon as it leaves the marina, it throttles up and moves with a constant acceleration of 2.40 m/s2. What is the velocity of the boat after acceleration of 5.00 seconds? B) How far does the boat travel in this time? 3) A ball is free falling towards the ground. Does its acceleration increase, decrease, or remain constant? Explain your answer using complete sentence.

HW Problems pg. 60

Pg 60 answers 1a -42 m/s 1b = 11 s 2a vf = -22 m/s 2b t = 2.2 (s)

A Olympic athlete hits a volley ball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0 m above the floor, how long will the ball be in the air before it strikes the floor? t = 1.5 s

Compare your reaction time with that of a friend by catching the ruler that is dropped between your fingers. Let your fined hold the ruler as shown in the figure.

Snap your fingers shut as soon as you see the ruler release Snap your fingers shut as soon as you see the ruler release. On what does the number of centimeters that pass through your fingers depend? Find the reaction time in second by solving Δy = ½ g t2: for time t= Sqare root ( 2Δy/ g Compare your reaction time with your class mates.