One Dimensional Motion

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One Dimensional Motion
HONORS PHYSICS: Chapter 2 Notes One Dimensional Motion 8/29/2014 Honors Physics Fall, 2014 Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Vector quantities Anything with MAGNITUDE and DIRECTION is termed a vector quantity Scalar quantities just have magnitude Gravity propels a skier down a snow-covered slope at an acceleration approximately constant. The equations of “KINEMATICS”, as studied in this chapter, can give his position and velocity at any given time Cunnings, Fall, 2014

Position, Distance, and Displacement
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Position, Distance, and Displacement Coordinate system  defines position Distance  total length of travel (SI unit = meter, m) Scalar quantity Displacement  change in position Cunnings, Fall, 2014

Position, Distance, and Displacement
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin and a positive direction. The distance is the total length of travel; if you drive from your house to the grocery store and back, what is the total distance you traveled? Displacement is the change in position. If you drive from your house to the grocery store and then to your friend’s house, what is your total distance? What is your displacement? Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Cunnings, Fall, 2014

Average speed and velocity
HONORS PHYSICS: Chapter 2 Notes Average speed and velocity 8/29/2014 Average speed = distance / time Average velocity  displacement divided by the total elapsed time Cunnings, Fall, 2014

Average speed and velocity
HONORS PHYSICS: Chapter 2 Notes Average speed and velocity 8/29/2014 What’s his average velocity if he returns to his starting point? What is his average velocity if he sprints 50 m in 8 s? What’s his average velocity if he walks back to the starting line in 40 s? Cunnings, Fall, 2014

Displacement and Velocity in One Dimension
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Displacement Time taken Displacement and Velocity in One Dimension Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Cunnings, Fall, 2014

Graphical Interpretation of Velocity
HONORS PHYSICS: Chapter 2 Notes Graphical Interpretation of Velocity 8/29/2014 The left graph shows a car moving at constant velocity (linear). The graph on the right shows a car with changing velocity. The average velocity for a given time interval is the slope of the line connecting the two coordinates in question. Cunnings, Fall, 2014

Graphical Interpretation of Average Velocity
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Graphical Interpretation of Average Velocity The same motion, plotted one-dimensionally and as an position vs. time (x-t) graph: Position vs time graphs give us information about: average velocity  slope of a line on a x-t plot is equal to the average velocity over that interval Cunnings, Fall, 2014

Graphical Interpretation of average velocity
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Graphical Interpretation of average velocity What’s the average velocity between the intervals t = 0 s  t = 3 s? Is the velocity positive or negative? What’s the average velocity between the intervals t = 2 s  t = 3 s? Is the velocity positive or negative? Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Which object is moving with constant POSITIVE velocity? Which is moving with NEGATIVE velocity? Which isn’t moving? HOW DO YOU KNOW? Cunnings, Fall, 2014

Instantaneous Velocity
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Instantaneous Velocity Instantaneous velocity This means that we evaluate the average velocity over a shorter and shorter period of time Cunnings, Fall, 2014

Instantaneous velocity
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 If we have a more complex motion… This plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is the SLOPE OF THE LINE tangent to the curve. Cunnings, Fall, 2014

Instantaneous velocity
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Average velocity is the slope of the straight line connecting two points corresponding to a given time interval Instantaneous velocity is the slope of the tangent line at a given instant of time Cunnings, Fall, 2014

Instantaneous velocity
HONORS PHYSICS: Chapter 2 Notes Instantaneous velocity 8/29/2014 Is the Instantaneous velocity at t = 0.5 s Greater than Less than Or equal to the instantaneous velocity at t =1.0 s? How do you know? Cunnings, Fall, 2014

Displacement and Velocity in One Dimension
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Displacement and Velocity in One Dimension Are the plots shown at the left correctly related A) YES B) NO CAN YOU EXPLAIN WHY?!?! THERE’S ROOM OVER THERE  YOU KNOW… Cunnings, Fall, 2014 18

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? A B C Cunnings, Fall, 2014 19

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Acceleration Average acceleration  the change in velocity divided by the time it took to change the velocity Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
Acceleration HONORS PHYSICS: Chapter 2 Notes 8/29/2014 On Earth, gravitational acceleration equals about 10 m/s/s What does it mean to have an acceleration of 10 m/s2 ? Time (s) Velocity (m/s) 1 10 2 20 3 30 Cunnings, Fall, 2014

Graphical interpretation of Acceleration
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Graphical interpretation of Acceleration Cunnings, Fall, 2014

Important Point Regarding Acceleration
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Important Point Regarding Acceleration When an object’s velocity and acceleration (both vector quantities) occur in the same direction, the object is SPEEDING UP!!!! When an object’s velocity and acceleration occur in opposing directions, the object is SLOWING DOWN!!! Deceleration is used to refer to a decrease in speed Don’t confuse “negative acceleration” with deceleration…PLEASE!! Cunnings, Fall, 2014

Instantaneous Acceleration
HONORS PHYSICS: Chapter 2 Notes Instantaneous Acceleration 8/29/2014 Very similar to “instantaneous velocity” from our position vs. time graphs a = lim Δv / Δt t0 The closer Δt gets to zero, the closer our ratio gets to a fixed number. Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
Acceleration HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Cunnings, Fall, 2014 25

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Velocity vs time (v-t) graphs give us information about: average acceleration, instantaneous acceleration the “+” 0.25 m/s2 means the particle’s speed is increasing by 0.25 m/s every second Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time? A B Cunnings, Fall, 2014 28

1-D Motion with constant acceleration
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 1-D Motion with constant acceleration When an object moves at constant acceleration, the instantaneous acceleration at any point in a time interval equals the average acceleration divided by the whole time interval In other words, with constant acceleration: Average acceleration is no different than instantaneous acceleration! Cunnings, Fall, 2014

Motion with constant acceleration
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 Motion with constant acceleration If the acceleration is constant, the velocity changes linearly: Average velocity: v0 = initial velocity a = acceleration t = time Cunnings, Fall, 2014

Constant Acceleration
HONORS PHYSICS: Chapter 2 Notes Constant Acceleration 8/29/2014 constant a(t) = a Cunnings, Fall, 2014 31

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Finding Displacement on a graph not using the origin as initial coordinates What this graph shows is the geometrical interpretation of the following equation! Cool, huh?! Cunnings, Fall, 2014

Freely Falling Objects
HONORS PHYSICS: Chapter 2 Notes Freely Falling Objects 8/29/2014 All objects fall towards earth at the same constant acceleration Assuming air resistance is zero, of course!! Any object moving upward, downward, or released from rest under the influence of gravity is considered “free falling” A football in the air, skydiver, falling book, etc. Cunnings, Fall, 2014

Motion with constant acceleration
HONORS PHYSICS: Chapter 2 Notes 8/29/2014 An object falling in air is subject to air resistance (and therefore is not freely falling). Free fall is the motion of an object subject only to the influences of gravity…in most cases we’ll consider, air resistance is negligible and can be ignored. Cunnings, Fall, 2014

HONORS PHYSICS: Chapter 2 Notes
8/29/2014 Free falling objects Free fall from rest: You could use the kinematics equations to see where the numbers are coming from, fyi!!! Cunnings, Fall, 2014

Trajectory of a projectile
HONORS PHYSICS: Chapter 2 Notes Trajectory of a projectile 8/29/2014 Cunnings, Fall, 2014