| the definition of speed: vav ≡ Δd / Δt vav x Δt = Δd |
to get an average (assuming uniform acceleration) vav = vinitial + vfinal / 2 if vinitial = 0, then vav = 1/2 vfinal |
(1) (2) |
| substituting for vav from (2) 1/2 vfinal x Δt = Δd |
(3) |
|
| according to Galileo, acceleration is... a ≡ Δv / Δt |
but change is always the difference: Δv = vfinal - vinitial |
(4) |
| so substituting Δv from (4), a = vfinal - vinitial / Δt if vinitial = 0, then a = vfinal / Δt a x Δt = vfinal |
(5) (6) (7) |
|
| substuting (7) into (3) 1/2 ( a x Δt ) x Δt = Δd 1/2 a Δt2 = Δd |
(9) (10) |
So the distance a falling object transverses, Δd, is proportional to the SQUARE of the elapsed time, Δt, multiplied by a constant, 1/2 a,
presuming acceleration is constant as Galileo claims, and measurements of t, d and vinitial are made from rest.
return to lab I-2
to ie-Physics menu
to site menu
