# Linear Motion Notes

1. Want: list variable names:
• Δt - how long, how much time, time passed
• Δx - how far, change in position or height
• xi - starting position or height
• xf - ending position or height
• vavg - "average" velocity
• vi - starting velocity, from this speed, velocity originally going at
• vf - ending velocity, to this speed; velocity it hit the ground with
• Δv - change in velocity, increase or decrease in speed, vf - vi
• 0 m / s: "at rest", "still", "unmoving", "released" (vi), "stopped" (vf), ball at top of throw
• a - acceleration, change in velocity per second, rate speeding up or slowing down at
2. Have: Variable names, numbers, units
3. Convert everything to m, s, kg using factor-label.
 1000 m = 1 km      60 s = 1 min      1000 g = 1 kg1000 mm = 1 m      60 min = 1 h100 cm = 1 m10 mm = 1 cm

4. Equation in which you know everything except one of your "wants."
EquationVariables
Δx = xf - xiΔx, xf, xi
Δt = tf - tiΔt, tf, ti
Δv = vf - viΔv, vf, vi
vavg = (Δx)/(Δt)vavg, Δx, Δt
a = (Δv)/(Δt)a, Δv, Δt
vf = vi + aΔta, vf, vi, Δt
Δx = .5(vf+ vi)ΔtΔx, vf, vi, Δt
Δx = viΔt + .5a(Δt)2Δx, Δt, a, vi

Can't find an equation that gets what you want? Find something else you can solve for. Having Δt might open up a whole new world of possibilities.
5. Plug in and solve.
• Don't plug in the units unless you're really comfortable with them - they can confuse you, and you already know what units you expect to come out.
• First simplify any expression that just has numbers in it. Cross out anything times zero. Cross out any "+ 0."
• Variable stuck on the bottom? Multiply both sides by it.
• Variable, or square of variable, encumbered by some coefficient multiplied by it? Divide both sides by the coefficient.
• Got the square alone on a side? Square root both sides.