Linear Motion 1-Dimensional Kinematics

Notation—physics vocab is concise d = distance x= location t = time ∆ (delta)= change s = speed= d/ ∆t ∆x= change in position V= velocity= ∆x / ∆t Subscripts: i, f i= initial, f= final

Motion is Relative Frame of Reference –Define Origin / X & Y axes Earth: Surface vs. Center X Y

Speed Speed = Distance / time Units: miles/hr; km/hr; m/s Average Speed = Total Distance / total time Instantaneous Speed = Interval distance / interval time EX: ROAD TRIP to U of I! Cow, Corn, & Soybeans…

Velocity Velocity = Speed with Direction! Velocity is a Vector Vector = Magnitude (size) + Direction Units: miles/hr; km/hr; m/s v = velocity x = change in position (displacement) t = time

Constant Velocity man covers same distance every second in the same direction ! his actual speed & direction are what’s constant!

Find the velocity of travel (e.g.travelocity?): Find the velocity of travel (e.g.travelocity?): 1. Run 20 m east in 2 sec m east in 1 sec, then 10 m west in 1 sec 3. run 15 m east, then 5 m west in 2 seconds 4. run 440 m (1 complete circle) in 44 seconds

Acceleration Acceleration = change in Velocity / time (How fast you change how fast your going!) Vector = Magnitude (size) + Direction Units: mi/hr/sec; m/s/s; m/s 2 a = acceleration v = change in velocity (final – initial) t = time

Constant acceleration woman covers more distance every second in the same direction her change in speed is what’s constant!

Problem Solving Physics of Legend 4 steps 1.Draw a Picture – VisualizeVisualize 2.Knowns and Unknowns – Know thy EnemyKnow thy Enemy 3.Equation – Select Secret WeaponSelect Secret Weapon 4.Solve for Unknown – Attack!!!Attack!!!

Free Fall Movement solely under the influence of gravity Acceleration due to gravity = g g = -9.8 m/s 2 = -32 ft/s 2 = -22 mi/hr/s!

Equation I Start with definition of acceleration: Rearrange to solve for v f : Traditional form: How fast you end up going is equal to how fast you were going, plus the rate of acceleration multiplied by the time of acceleration!

Equation II Start with definition of velocity and solve for x: If acceleration is constant then substitute for v: Traditional form: How far you have traveled is equal to your average rate of travel (average velocity) multiplied by time!

Combine like terms and distribute t: Equation III Start with Equation I and substitute into Equation II to eliminate v f : Final form: How far you end up going is equal to how fast you were going multiplied by time, plus one-half the rate of acceleration multiplied by the time squared!

Final Form: Distribute factors and combine like terms: Equation IV Rearrange Equation I and substitute into Equation II to eliminate t: The final velocity squared is equal to the initial velocity squared plus two times the acceleration times the displacement!

a = acceleration x = change in position (displacement) v f = final velocity v i = initial velocity t = time interval of motion T he N ifty E quations O f M otion (The Kinematic Equations for Constant Accelerated Motion!) Equationat vivivivi vfvfvfvf          

Free Fall Speeds & Distances How FAST = Rearrange acceleration equation to solve for v f : How FAR = equation for free fall distances when falling from rest: x = change in position (displacement) a = acceleration t = time

TNEOM’s from graphs Displacement X= area under v-t curve X = rectangle + triangle area X = Vi * t + ½*(Vf- Vi)*t Substitute : a = (Vf- Vi )/t or (Vf-Vi)= a*t X = Vi*t + ½*a*t 2 Velocity Vf V i time