CH4 Linear Motion with Uniform Acceleration Physics (A) Winter,

Relative Motion An object is moving if its position relative to a fixed point is changing. Ex. Are you moving when: you are sitting in a moving car? ANS. YES, relative to ground NO, relative to the driver’s seat running down the street? ANS. YES, relative to the ground NO, relative to your shoes you are watching a city bus drive by? ANS. NO, but the bus is relative to you/ground NO, but the passengers are relative to you/ground 2

Speed Speed = change in distance/change in time Symbol is v Units: m/s “meters per second” / sign = per Scalar Quantity: a # with NO DIRECTION SAME AS VELOCITY BUT IGNORE DIRECTION! Ex. You drove 40 mi/hr this morning on Eureka Rd 3

Velocity Velocity = change in distance/change in time Symbol is v Units: m/s “meters per second” / sign = per Vector Quantity: value has magnitude AND direction (N,S, up, down, etc.) SAME AS SPEED BUT DIRECTION MATTERS! Ex. You drove 40 mi/hr eastbound this morning on Eureka Rd 4

Speed & Velocity Speed/Velocity - the rate of change in position over time (distance/time) Instantaneous speed: Your speedometer Average speed: v avg : Δ d (Eq. 5) Δ t Ex. You traveled from Southgate to Westland (18 mi) in 1 hour, for an avg. speed of 18 mi/hr How is velocity different from speed? 5

Change in Velocity What causes an object to change velocity? 3 THINGS CAN CAUSE IT: 1. Change in Speed 2.Change in Direction 3.Change in BOTH 6

Acceleration Acceleration = change in velocity/change in time Symbol is a Units: m/s 2 “meters per second squared” Vector Quantity: value has magnitude AND direction (N,S, up, down, etc.) Ex. You accelerated at 4 m/s 2 eastbound this morning on Eureka Rd Can be positive or negative, accels = positive, decels = negative Uniform Acceleration=constant acceleration Ex. g=9.8 m/s 2 7

Kinematic Equations for Uniform Acceleration v f = v i + a∙t(Eq. 6) ∆d = ½(v f +v i )t(Eq. 7) ∆d=v i ∙t + ½∙a ∙t 2 (Eq. 8) v f 2 =v i 2 + 2∙a∙d(Eq. 9) 8

Delta ∆ is “Delta” on greek alphabet. It means “difference” ∆ gives you the right to subtract. In Science, ∆ = Final - Initial 9

Free Fall Free Fall = object is under the influence of force of gravity ONLY Elapsed Time (ET) = Δt=time an object starts to fall/move to time object stops to fall/move All objects fall on Earth at a=g=9.8 m/s 2 NEVER NEVER NEVER ESTIMATE/APPROXIMATE g!!!!!!! 10

Air Resistance When an object falls, is the force of gravity, the only force acting on the object? NO! Air resistance, a form of friction, is acting in OPPOSITE direction of force of gravity 11

Graphs of Motion- Velocity Plot 12

Graphs of Motion- Velocity Plot Graph is Linear (straight line) Slope = m = rise run Slope of Speed/Velocity Graph = CONSTANT ACCELERATION, a 13

Graphs of Motion- Distance Plot 14

Graphs of Motion- Distance Plot Graph is NON-linear (parabola) Slope = m = rise run Slope of Distance Graph = INSTANTANEOUS SPEED, v 15

Math Practice Ex. If your average speed is 40 km per hour and you have traveled for 0.5 hour, what distance have you traveled? GIVEN: Vavg = 40 km/h Δt = 0.5 h UNKNOWN: Δd = ? EQUATION: Vavg = Δ d Δ t PLUG-IN: 40 km/h = Δ d 0.5h SOLVE: Δd = 20 (km) 16

Problem Solving Flashcard! 1. Circle what the question is asking you to find (less than 3 words!). Put the symbol for this phrase under Unknown: section. 2.Read problem and list all of your GIVENS as their symbols NOT words under GIVEN: section. 3.Go to your formula sheet and pick a formula that has ALL GIVENS AND UNKNOWN in it. Write it under FORMULA: section. 4.Under PLUG-IN: section, plug-in what you know (from GIVENS and UNKNOWN) EXACTLY WHERE YOU FIND IT IN FORMULA. 5.Using Algebra, solve for missing variable with units, under the SOLVE: section. 6.Circle your answer. 17