y kx 2 parabolic exponential proportion distance is

y= kx 2 parabolic exponential proportion distance is proportional to time squared d = kt 2 2= k cm/s Unit analysis constant acceleration

linear direct proportion 2*distance is directly proportional to time squared y = kx Unit analysis 2 d = kt 2 cm/s 2= k constant acceleration

linear direct proportion velocity is directly proportional to time y = kx Unit analysis vf = kt cm/s 2= k constant acceleration

The work of Galileo set up a plane with a small angle of inclination. He rolled a ball down the plane and measured the times for different distances. (water clock) He then extrapolated his results for acceleration down the plane to the vertical.

Why use an incline to study the effects of gravity? What would have been a better way to measure acceleration due to gravity? drop something !!!!! Why didn’t Galileo do this? He couldn’t measure the time

Earth’s Gravity (g) 9. 8 m/s 2 = 980 cm/s 2 = 2 32 ft/s Acceleration due to gravity on the Earth’s surface is uniform Galileo showed - All objects fall at the same rate REGARDLESS of their mass !!!

1) 2 d t 2 0 0 1. 7 1. 300 6. 8 3. 881 15. 3 9. 242 27. 2 17. 48 42. 5 25. 91 a) It shows that the ball b) rolled with a constant c) acceleration b) Slope ≈ 1. 6 m/s 2 c) g = 1. 6 ÷ sin 10° d) g ≈ 9. 21 m/s 2 2 d (m) d) t 2 (s 2) 6. 0%

2) First of all, where do these equations come from? d = vit +½at 2 d = ½at 2 vi = 0 (starts from rest) vf = vi + at vf - vi = a v = a t t rearranging Galileo couldn’t measure velocity!!!

3) First of all, where do these equations come from? d = v avg t d = vavgt Can’t plug a final velocity in for an average velocity vf = vi + at v = at f vi = 0 (starts from rest)

4) Given: vi = 22 m/s vf = 55 m/s t = 11 s a = ? m/s 2 d = ? m 5) Given: vi = 0 m/s vf = 40 m/s t = 9. 5 s d = ? m vf = vi + at 55 = 22 + (a)(11) a = 3. 0 m/s 2 2 d = (vf + vi)t 2 d = (55+22)(11) 2 d = (vf + vi)t 2 d = (40+0)(9. 5) d = 424 m d = 190 m

6) Given: g = a ÷ sinθ vi = 12 m/s 2 d = v t +½at i a = -1. 6 m/s 2 t = 6 s; 9 s d = 12(6) + ½(-1. 6)(6)2 d = ? m d = 12(9) + ½(-1. 6)(9)2 9. 4° d = 43. 2 m What’s the deal with that? It’s at the same spot two times (once on the way up the ramp, and once on the way down) Who can tell me the angle of the incline?