Aim: How can we use additional physics formulas?

1. Aim: How can we use additional physics formulas? Do Now: List the three physics formulas previously learned

2. Physics Formulas Previously learned: New formulas: Or is it? These are new These are the same (t) (t)

3. Problems • A ball, initially at rest, rolls with a constant acceleration of 2 m/s2. • What is the final velocity after rolling 10 m? • Given • vi = 0 m/s • a = 2 m/s2 • d = 10 m • vf = ? Choose an appropriate formula vf2 = (0 m/s)2 + 2(2 m/s2)(10 m) vf2 = 40 vf = 6.3 m/s

4. b. How long did it take the ball to roll 10 m? 2 options: • Given • vi = 0 m/s • a = 2 m/s2 • d = 10 m • vf = 6.3 m/s • t = ? 6.3 m/s = 0 m/s + (2 m/s2)t 6.3 = 2t 2 2 t = 3.15 s or 10 m = (0 m/s)t + ½(2 m/s2)t2 10 = t2 t = 3.15 s

5. 2. A runner, initially at rest, accelerates at a rate of 1.5 m/s2 for 100 m. a. How long did the race take? Given vi = 0 m/s a = 1.5 m/s2 d = 100 m t = ? 100 m = (0 m/s)t + ½(1.5 m/s2)t2 100 = 0.75t2 t = 11.5 s

6. b. What was the runner’s final velocity? Given vi = 0 m/s a = 1.5 m/s2 d = 100 m t = 11.5 s vf = ? vf = 0 m/s + (1.5 m/s2)(11.5 s) vf = 17.3 m/s or vf2 = (0 m/s)2 + 2(1.5 m/s2)(100 m) vf2 = 300 vf = 17.3 m/s

7. 3. An airplane approaches a runway with an initial velocity of 5 m/s. After accelerating at a rate of 8 m/s2 for 12 s, the plane takes off. a. What distance did the plane travel on the runway? Given vi = 5 m/s a = 8 m/s2 t = 12 s d = ? d = vit + ½at2 d = (5 m/s)(12 s) + ½(8 m/s2)(12 s)2 d = 60 + 576 d = 636 m

8. b. What was the final velocity of the plane at takeoff? Given vi = 5 m/s a = 8 m/s2 t = 12 s d = 636 m vf = ? vf = 5 m/s + (8 m/s2)(12 s) vf = 101 m/s or vf2 = (5 m/s)2 + 2(8 m/s2)(636 m) vf2 = 10,201 vf = 101 m/s

9. Pages 64-67