Freefall and “The Kinematic Equations” a.k.a. “Four Equations Of Constant Acceleration”

Sample Problem Consider the following series of speeds for an accelerating object. The speeds were recorded at 1-second intervals. 20m/s, 25m/s, 30m/s, 35m/s, 40 m/s, 45m/s, 50m/s What is the average speed during the acceleration?

Possible Variables to Solve for with Acceleration: vi = initial velocity (m/s) vf = final velocity (m/s) a = acceleration (m/s2 or m/s/s) t = time (sec) Δ d = displacement Sign Conventions: Conventionally, signs are: Up &/or Right = positive Down &/or Left = negative Your numbers must have the correct signs when plugging into the kinematic equations! You can make any direction positive or negative, as long as you are consistent in the problem!!

“The Four Equations of Constant Acceleration” no ‘d’ no ‘a’ no vf no ‘t’

Kinematics – Sample Problem Starting from rest, a racecar travels 201 m in the first 5.0 seconds of acceleration. What is the car’s acceleration? vi=0 m/s d=201 m t= 5.0 s a=? 201 m = 0 + (0.5 )a(52 s) a = 16.08 m/s

Kinematics – Sample Problem An engineer is to design a runway to accommodate airplanes that must gain a ground speed of 60.0 m/s before they can take off. These planes are capable of acceleration at the rate of 1.5 m/s2. What is the minimum distance the planes need to take off?

Sample Problems Work sample problems in your notes.

Acceleration Due to Gravity Galileo found that in the absence of air resistance, all objects dropped near the surface of a planet will fall with the same acceleration. Freely falling bodies undergo constant acceleration Acceleration on earth due to gravity = 9.8 m/s2

Freefall Motion For the purpose of this class, we will “consider a spherical cow.” HUH??? In other words, we will neglect air resistance for problems involving constant acceleration.

Freefall Motion g = 9.8 m/s2 and agravity = -9.8 m/s2 Acceleration on earth due to gravity = 9.8 m/s2 Positive or negative? Gravity pulls everything DOWN “g” will differ on other planets, and can be calculated In our calculations, g = 9.8 m/s2 and agravity = -9.8 m/s2

Problem Predict the velocity of the falling ball at the indicated time intervals. t=0 vi = 0 m/s t=2 v2 = vi + at = 0 + (-9.8)(2) = -19.6 m/s v4 = vi + at = 0 + (-9.8)(4) = -39.2 m/s t=4

Problem Vanessa Vandal throws a brick from a high scaffold with an initial downward speed of 1.5 m/s. What is its velocity after falling for 3.5 s? no ‘d’ no ‘a’ no vf no ‘t’

Problem Trixie Truelove drops a penny into a wishing well that is 10 meters deep. How many seconds will it take to hit bottom?

Problem Clifton Klutz falls from a 25 meter high cliff. What is his velocity just before he hits the water?

Problem Dizzy Dimwit decides to fly by jumping off a water tower. How many seconds will he fall before reaching a downward speed of 25 m/s?

Extra Freefall Problems 1. A brick is dropped from the roof of a building under construction. The brick strikes the ground after 4.85 seconds. What is the brick’s velocity just before it reaches the ground? no ‘d’ no ‘a’ no vf no ‘t’

Extra Freefall Problems 2. How tall was the building from #1? no ‘d’ no ‘a’ no vf no ‘t’

Activity Experimentally Find “g” Experimentally determine the acceleration of gravity using: 2 photogates and timer 1.8-cm diameter marble Ruler Pole and blue knob Your brain Hint #1: Balance the ball at the end of the blue knob to guarantee that the widest part falls through the IR beams. Hint #2: Organize your work in the GFWA method so that you know what you’ve got Hint #3: +/- signs matter! Hint #4: There are multiple ways to solve this problem!

I’m now allowing you to throw things… Throw a tennis ball up into the air. Describe the ball’s path, its velocity, and its acceleration. I will be calling on a group to give their answer, so be prepared to speak.

What Goes Up…… When we throw an object up into the air, it: Continues to move upward for some time Stops momentarily at its peak Changes direction and begins to fall Velocity is continually changing

What about the Acceleration? Acceleration is CONSTANT! Objects thrown into the air have a downward acceleration as soon as they are released. This is what causes them to slow down as they go up, and speed up as they fall back down!

Path of Tennis Ball ZERO - + - + - - SAME BUT OPPOSITE Velocity is _______ at top Upward trip Downward trip - + Direction of d Direction of v Direction of a Direction of d Direction of v Direction of a - + - - SAME BUT OPPOSITE Velocity is _________ at bottom

Sample Problem A bullet is shot vertically upward with an initial velocity of 588 m/s. How high will it go?

Sample Problem A gazelle is playing catch with itself by kicking a ball straight up. How fast does he kick the ball if it comes back to his foot 2.5 seconds later?

Sample Problem A flowerpot falls past a window and hits the ground 130 meters below the window. If it took 3.5 seconds for the pot to fall the 130 m to the ground, how fast was the flowerpot going when it passed the window?

Sample Problem Assuming the flowerpot’s initial velocity (v0) was zero, from what height was the flowerpot originally dropped?

Sample Problem DOH! Homer Simpson fires a Daisy BB gun at 720 ft/sec straight up into the air. How high will the BB go? How long will it remain airborne?

Sample Problem A ball thrown vertically upward returns to its starting point in 2.47 seconds. What was its initial velocity?

Activity: Height of the Room Using a tennis ball, timer, and meter stick, calculate (A) the initial velocity needed to barely touch the ceiling (B) the height of the room. Hints: Make sure the ball just barely hits the ceiling tile Check your precision! Don’t forget about your own height Use GFWA method