Motion in One Direction Motion in One Direction Chapter 2 Chapter 2

Goals: motion, displacement, velocity, Goals: motion, displacement, velocity, acceleration, freefall, acceleration due acceleration, freefall, acceleration due to gravity and equations to solve for to gravity and equations to solve for

velocity, acceleration and displacementvelocity, acceleration and displacement

Section 2.1 Displacement and Section 2.1 Displacement and velocityvelocity

Distance- space between two points, Distance- space between two points, one dimension, length, measured in one dimension, length, measured in meters (scalar) Total change in meters (scalar) Total change in positionposition

Displacement- space between two Displacement- space between two points in one direction, length, points in one direction, length, meters, pos or neg (vector) meters, pos or neg (vector) Net change in position Net change in position

ΔΔX= X X= X ff– X– Xii

VelocityVelocity Velocity- rate of displacement speed?Velocity- rate of displacement speed? rates occur in a unit of time secondsrates occur in a unit of time seconds velocity = displacement / timevelocity = displacement / time v = v = ΔΔX / t m/sX / t m/s Graph time on X and position on YGraph time on X and position on Y Instantaneous velocity is a point on a graphInstantaneous velocity is a point on a graph Average is the total displacement per unit Average is the total displacement per unit

of timeof time Graph Velocities pos (upward curve), Graph Velocities pos (upward curve),

stationary (horizontal curve), neg stationary (horizontal curve), neg (downward curve)(downward curve)

Section 2.2 AccelerationSection 2.2 Acceleration What is any change in velocity?What is any change in velocity? Acceleration- rate of change in velocityAcceleration- rate of change in velocity change in velocity per unit of timechange in velocity per unit of time a = a = ΔΔv / t = v f – v i/ tv / t = v f – v i/ t m / sm / s2 2

positive or negativepositive or negative average acceleration = v f + v i/ 2 average acceleration = v f + v i/ 2

v = v = ΔΔx / t x / t ΔΔx = x = ½ (vf + vi) t ½ (vf + vi) t

Graphing acceleration time on x and velocity on yGraphing acceleration time on x and velocity on y pos (upward slope), constant velocity (horizontal curve), pos (upward slope), constant velocity (horizontal curve),

neg (downward curve)neg (downward curve) What if you had……………………………..What if you had…………………………….. pos v and pos a ?pos v and pos a ? right! object is speeding upright! object is speeding up pos v and neg a ?pos v and neg a ? right! object is slowing downright! object is slowing down neg v and neg a ?neg v and neg a ? right! object is speeding upright! object is speeding up neg v and pos a ?neg v and pos a ? right! Object is slowing downright! Object is slowing down what about 0 v and 0 a ?what about 0 v and 0 a ? the object is stillthe object is still what about 0 a ?what about 0 a ? the object has constant velocity (like terminal v)the object has constant velocity (like terminal v)

Section 2.3 Free FallSection 2.3 Free Fall Why do objects fall? Accelerate towards Why do objects fall? Accelerate towards

EarthEarth Remember: acceleration is a rate of change Remember: acceleration is a rate of change

in Velocity due to an unbalanced forcein Velocity due to an unbalanced force Unbalanced forces cause accelerationsUnbalanced forces cause accelerations Gravity and Air Friction are the unbalanced Gravity and Air Friction are the unbalanced

forcesforces Gravity is a force of attraction accelerating Gravity is a force of attraction accelerating

all objects in freefall towards Earthall objects in freefall towards Earth acceleration due to gravity is a constant acceleration due to gravity is a constant

and known to be -9.81 m/sand known to be -9.81 m/s2 2 g= 9.81 m/sg= 9.81 m/s22

use little “g” for “a” in problems use little “g” for “a” in problems involving freefall involving freefall

In conclusion:In conclusion: we considered the following variables:we considered the following variables: x v a g x v a g ΔΔx for change in displacement xx for change in displacement xf f - x- xii ΔΔt for change in time tt for change in time tff - t - ti i a for acceleration a for acceleration ΔΔv/v/ΔΔtt we also considered average velocity we also considered average velocity

v vf f + v+ vi i / 2 so we can calculate average / 2 so we can calculate average acceleration in m/sacceleration in m/s22

and derived equations for calculating and derived equations for calculating displacement displacement ΔΔx=1/2 (vx=1/2 (vff+v+vii) t if you are ) t if you are given “v” and “t” or given “v” and “t” or ΔΔx=vx=viiΔΔt + 1/2a(t)t + 1/2a(t)22 if if you are given acceleration and time you are given acceleration and time

or if you want to find velocity which or if you want to find velocity which is: v=a times t use these is: v=a times t use these derivatives: vderivatives: v ff= v= vii + a + a (t) or v(t) or vff

2 2 =v=vii22 + 2 a + 2 a ΔΔx x

QuestionQuestion What is so great about Physics?What is so great about Physics? AnswerAnswer Physics is ACCELERATING!Physics is ACCELERATING!