Physics 40 Chapter 2 1-D Kinematics

Natural Motion Objects have a proper place Objects seek their natural place The heavier the object, the faster it falls. Did not experiment to test theories.

The natural motion of a body is to remain in whatever state of motion it is in unless acted upon by net external forces. Galileo Challenged The Dogma Of Natural Motion

Galileo Challenged The Dogma Of Natural Motion with Experiments

Galileo Challenged Aristotle Physics In a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s 2, independent of their weight.

Galileo’s Motion Studies What causes a rolling ball to stop? What causes the ball to speed up? What causes the ball to slow down? gravity friction

Galileo’s Motion Studies gave us… Definitions: From these we derive the kinematics equations….

Start: Combine & Eliminate t: Algebra:

Galileo’s Motion Studies gave us… Kinematic Equations

Newton’s Calculus gave us…

Uniform Motion in a nutshell Motion with constant acceleration.

Distance and Displacement The total distance traveled relative to an origin. Distance is a scalar. Displacement is a vector. The unit is the meter.

Average Speed &Velocity Speed is how fast something moves. The average speed is the total distance per time. The average velocity is the the total displacement per time. Velocity is a vector. The unit is m/s.

Acceleration How fast How fast is changing. The rate at which the speed is changing. Speeding up Slowing down Constant speed, changing direction.

Acceleration is in the direction of the net Force but not necessarily in the direction of velocity. Velocity is always in the direction of the motion!

Sense of Speed

Quicky Question An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s. a) What is the automobile’s average velocity? Which equation?

An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s. b) What is the automobile’s average acceleration? Which equation? Quicky Question

An automobile enters a freeway on-ramp at 15.0m/s and accelerates uniformly up to 25.0 m/s in a time of 10.0s. c) What is the distance traveled in this amount of time? Which equation? Quicky Question (you could also use v ave equation.)

Acceleration: Changing Velocity QUESTION: From t = 0, how long does it take the car to come to a full stop? +x YOU TRY IT!

Acceleration: Changing Velocity Which equation to use? Solve for t:

Acceleration: Changing Velocity From t = 0, to t = 5.6s, how far does the car travel before it comes to a stop? +x Which equation? YOU TRY IT!

What Goes Up Must Come Down Someone standing at the edge of a cliff throws one ball straight up and one straight down at the same speed. Ignoring air resistance, which ball strikes the ground with the greatest speed?

Brake Question You are driving a car going 80 km/hr (50mph) when a head-on collision happens 25 meters ahead of you. If you can brake at 6 m/s 2, will you hit the crash or stop before it? CRASH! Stopping Distance goes as the SQUARE of the speed!

Free Fall Unless told otherwise, ignore air resistance for free fall problems!

Acceleration of Freely Falling Object The acceleration of an object in free fall is directed downward, regardless of the initial motion The magnitude of free fall acceleration is g = 9.80 m/s 2 –g decreases with increasing altitude –g varies with latitude –9.80 m/s 2 is the average at the Earth’s surface –We will neglect air resistance

Free Fall Equations For any object in the absence of air resistance. Note: v 0 can be negative! (taking up as +y)

Falling from Rest + How FAR is not How FAST! Take down as +y:

How Far: y(t) ~ t 2 How Fast: v(t) ~ t 1 +

FIRST: Define Reference Frame In this reference frame,what is the sign of a? What is v at t = 3s? Negative because it is moving downward, in the negative direction!

FIRST: Define Reference Frame The displacement is negative because it is moves downward, in the negative direction but “how far” is a distance – a scalar – and is positive! How far did the ball fall in those 3 seconds? The ball fell 44.1m.

Free Fall Question: You throw the rock down with an initial speed of 30 m/s. The rock hits the ground in 3 seconds. With what velocity will the rock hit the ground? +y How high is the cliff?

Free Fall The cliff is 134 m high. +y Question: You throw the rock down with an initial speed of 30 m/s. The rock hits the ground in 3 seconds. With what speed will the rock hit the ground? How high is the cliff?

Free Fall: Throwing Up What is the speed at the top of the path? ZERO! What is the acceleration at the top? a = m/s 2 What is the velocity at the same height on the way down? -30 m/s +y With what velocity will the rock hit the ground? m/s SAME as if you threw it straight down at 30m/s!

How long does it take to hit the ground? First try to guess! +y How long to the top? How long back to launch point? Final v increases by 30m/s? I guess about 9 seconds! Free Fall: Throwing Up Problem

Symmetry of The G-Field

Motion Graphs

What kind of motion is this?

What is the velocity during each segment?

Average Velocity What is the average velocity between B and D?

Instantaneous Velocity The velocity at any time t is the slope of the x vs t graph at t. What is the instantaneous velocity at t=2.5s? What kind of motion does this graph represent? What does the velocity vs time graph look like?

Velocity Graph What does the a-t graph look like?

Acceleration Graph What does the a-t graph look like?

What is the displacement from zero to 2s? m/s (s) In general……

Displacement = area under the v-t graph

What is the displacement from zero to 2s? m/s (s)

What is the displacement from zero to 2s? Displacement = area under the v-t graph m/s (s) Zero!

What is the displacement from zero to 4s? Displacement = area under the v-t graph m/s (s)

HW Problem #46 Derive displacement equations for each segment.

HW # 60 Rock Drop A rock is dropped from rest into a well. The sound of the splash is heard 2.40 s after the rock is released from rest. How far below the top of the well is the surface of the water? The speed of sound in air (at the ambient temperature) is 336 m/s.

HW #32 Speedy Sue Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at  2.00 m/s 2 because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue's car and the van.

Hill Question On which of these hills does the ball roll down with increasing speed and decreasing acceleration? a) b) c) a)b) c)