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Transcript
CH4 Linear Motion with Uniform Acceleration Physics (A) Winter, 2010-2011 1 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: vavg: Δ d (Eq. 5) Δt • 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/s2 “meters per second squared” Vector Quantity: value has magnitude AND direction (N,S, up, down, etc.) • Ex. You accelerated at 4 m/s2 eastbound this morning on Eureka Rd • Can be positive or negative, accels = positive, decels = negative • Uniform Acceleration=constant acceleration Ex. g=9.8 m/s2 7 Kinematic Equations for Uniform Acceleration vf = vi + a∙t (Eq. 6) ∆d = ½(vf+vi)t (Eq. 7) ∆d=vi∙t + ½∙a 2 2 vf =vi + 2∙a∙d 2 ∙t (Eq. 8) (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/s2 • 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 MotionVelocity Plot 12 Graphs of MotionVelocity Plot • Graph is Linear (straight line) • Slope = m = rise run • Slope of Speed/Velocity Graph = CONSTANT ACCELERATION, a 13 Graphs of MotionDistance Plot 14 Graphs of MotionDistance 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 Δt 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