Physics Ch. 2: Motion Along a Straight Line

2.1) IMPORTANT NOTE: Properties discussed are of motion that is restricted by1. All straight line motion2. Forces behind the actual motion aren't discussed3. Moving object is either

a. Particlei. Point-like objectii. Eg. Electron

b. Something that moves like a particlei. Every portion of it moves in same direction and at same rate

2.2) Position and Displacement Locating an Object: Distance from reference point

o Origin (Zero point) Displacement: Change from one position x1 to another x2

o ∆x= x2 - x1

o Sign of result indicates direction of displacement, result without a sign is a magnitudeo Vector Quantity: Quantity that has both direction and magnitude

2.3) Average Velocity & Average Speed Average Velocity (vavg): Ratio of the displacement ∆x that occurs during a particular time interval ∆t to that

interval; result always equal to length over timeo vavg = (∆x / ∆t) = [(x2-x1) / (t2 - t1)]o vavg is the slope of the function of distance over time

Average Speed (savg): Total distance covered regardless of displacement over time (Has no sign)o savg = Total Distance / ∆t

2.4) Instantaneous Velocity & Speed Instantaneous Velocity/ Velocity: How fast a particle is moving at a given instant

o v = lim∆t->0(∆x / ∆t) = (dx / dt) Speed: The magnitude of velocity

2.5) Acceleration Average Velocity (vavg): Ratio of the displacement ∆x that occurs during a particular time interval ∆t to that

interval; result always equal to length over timeo vavg = (∆x / ∆t) = [(x2-x1) / (t2 - t1)]o vavg is the slope of the function of distance over time

Average Speed (savg): Total distance covered regardless of displacement over time (Has no sign)o savg = Total Distance / ∆t

2.5) Acceleration Acceleration: The rate at which something’s velocity is changing at a given instant; always length / time2

o Average Acceleration (aavg) = (v2 – v1)/(t2 – t1) = ∆v/∆to Instantaneous Acceleration/ Acceleration (a) = dv / dt

Combine this with v = (dx / dt) and you get a = (d / dt)(dx / dt) = (d2x / dt2) Acceleration is the second derivative of position x(t) with respect to time

o g units of acceleration: 1g= 9.8 m/s2

2.6) Constant Acceleration: A Special Case (Properties for Constant or Abt. Constant Acceleration) Can rewrite (v2 – v1)/(t2 – t1) = ∆v/∆t as a = aavg = (v – v0)/(t – 0) *v0 is the velocity at t = 0*

o v = v0 + at Basic Equations for Constant Acceleration

o Rewrite vavg = ∆x/∆t = (x2 – x1)/(t2 – t1) as vavg = (x – x0)/(t – 0) * x0 is the position at t = 0*o vavg = (v0 + v)/2 -> vavg = v0 + (at)/2 -( Sub x = x0 + vavgt)> x – x0 = v0t + (at2)/2 o Other Formable Equations

v2 = v02 + 2a(x - x0)

x - x0 = [(v0 + v)(t)]/2 x - x0 = vt - [(a)(t2)]/2

o Summary:Equation Missing Quantityv = v0 + at x - x0

x - x0 = v0t + [(a)(t2)]/2 vv2 = v0

2 + 2a(x - x0) tx - x0 = [(v0 - v)(t)]/2 ax - x0 = vt - [(a)(t2)]/2 v0

2.7) Calculus Derivation of [x - x0 = v0t + [(a)(t2)]/2]

2.8) Free-Fall Acceleration Free-fall Acceleration: Constant rate at which an object would fall w/o wind resistance

o Magnitude is represented by g Independent of object characteristics (mass, volume, density, etc.) Does vary a little bit due to latitude and/ or elevation

o Equations from 2.6 work for free-fall as well