1. You will be able to calculate Instantaneous speed Average speed Of falling or rising objects

2. Falling Objects In your own words what is “free fall”? 4.5 Free Fall: How Fast

3. An object is said to be in free fall when… – An object is moving under the influence of only the gravitational force.

4. What is elapsed time ? – The elapsed time is the time that has elapsed, or passed, since the beginning of any motion, in this case the fall.

5. Recall that acceleration is… The change in speed Time interval

6. During Free Fall Each second of fall the instantaneous speed of the object increases by an additional 10 meters per second due to the force of gravity. This gain in speed per second is the acceleration.

7. -about 10 meters per second squared (10 m/s 2 ) -The letter v represents both speed and velocity So g = 10 m/s 2 (the acceleration) Gravity is a constant it does not change!!! The acceleration of an object in free fall is

8. Although g varies slightly in different parts of the world, its average value is nearly 10 m/s 2. Where accuracy is important, the value of 9.8 m/s 2 should be used. Gravity is a constant it does not change!!! Note:

9. So let’s take a look at instantaneous speed of an object in free fall

10. If a falling rock were somehow equipped with a speedometer, in each succeeding second of fall its reading would increase or change by the same amount, 10 m/s. 4.5 Free Fall: How Fast

11. So… The instantaneous speed of an object falling from rest is equal to the acceleration multiplied by the elapsed time. v = gt Gravity is a constant it does not change!!!

12. For example If a police officer where to pull over the rock for speeding, while it was falling it would “clock” the rock at that instant. If it had been falling for 8 seconds what would its instantaneous speed be? Use the formula v = gt V=? g= t= Gravity is a constant it does not change!!!

13. Concept check In the space below you and your partner will define instantaneous speed in your own words Now solve the following: A rock falls for 3 seconds what is it’s instantaneous speed? If that same rock had an instantaneous speed of 50 m/s v g t

14. 4.5 Free Fall: How Fast v = gt

16. Practice If a skydiver was in “freefall” what would his velocity be after 10 seconds If a skydiver was in “freefall” traveling at 150m/s, how long was he falling? v g t

17. Rising Objects Now consider an object thrown straight up: Does the instantaneous speed change when an object moves upward rather than downward? It moves upward for a while. At the highest point, the object changes its direction from upward to downward, its instantaneous speed is zero. It then falls downward as if it had been dropped from rest at that height. 4.5 Free Fall: How Fast

18. During the upward part of this motion, the object slows from its initial upward velocity to zero velocity. The object is accelerating because its velocity is changing. How much does its speed decrease each second? Gravity is a constant it does not change!!! 4.5 Free Fall: How Fast

19. Bell Ringer: Answer the following What is the difference between “free fall” in terms of a skydiver versus “free fall” in terms of physics. What is the acceleration of gravity Explain what is meant by: “gravity is constant”

20. During the upward part of this motion, the object starts to slow from its initial upward velocity to zero velocity. The object is accelerating because its velocity is changing. (remember a change in speed or direction changes velocity) How much does its speed decrease each second? 10m/s 2 The change in speed each second is the same whether the ball is going upward or downward. 4.5 Free Fall: How Fast } } } }

21. The speed decreases at the same rate it increases when moving downward—at 10 meters per second each second. The instantaneous speed at points of equal elevation in the path is the same whether the object is moving upward or downward. The velocities are different because they are in opposite directions. During each second, the speed or the velocity changes by 10 m/s downward. 4.5 Free Fall: How Fast

22. Now let’s take a look at the average speed of an object in free fall

23. What if we want to know what our average speed is? Remember that when we find an average of something we add them, then divide by the number of items we added. Example: 2 + 6 = 8 the average is 4

24. The average speed of any object moving in a straight line with constant acceleration is the average of the initial speed and the final speed divided by 2. Or v i + v f 2 The average speed of a freely falling object in its first second of fall is the sum of the initial speed of zero and the final speed of 10 m/s, divided by 2, or 5 m/s. 4.5 Free Fall: How Fast So then what is the average speed of an object in free fall?

25. think! During the span of the second time interval in Table 4.2, the object begins at 10 m/s and ends at 20 m/s. What is the average speed of the object during this 1-second interval? What is its acceleration? 4.5 Free Fall: How Fast

26. think! During the span of the second time interval in Table 4.2, the object begins at 10 m/s and ends at 20 m/s. What is the average speed of the object during this 1-second interval? What is its acceleration? Answer: The average speed is 15 m/s. The acceleration is 10 m/s 2. Let’s work it out v = gtv i + v f g (a)= 2 t= v= 4.5 Free Fall: How Fast

27. think! What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? How about 8 seconds after it is dropped? 4.5 Free Fall: How Fast

28. think! What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? How about 8 seconds after it is dropped? Answer: The speedometer readings would be 45 m/s and 80 m/s, respectively. What would be the average speed? 4.5 Free Fall: How Fast

29. What is the acceleration of an object in free fall? 4.5 Free Fall: How Fast

30. For each second of free fall, does an object fall a greater distance than it did in the previous second? 4.6 Free Fall: How Far

31. How far does an object in free fall travel in the first second? At the end of the first second, the falling object has an instantaneous speed of 10 m/s. The initial speed is 0 m/s. The average speed is 5 m/s. This is the speed we need to calculate how far it falls During the first second, the object has an average speed of 5 m/s, so it falls a distance of 5 m. 4.6 Free Fall: How Far

32. Pretend that a falling rock is somehow equipped with an odometer. The readings of distance fallen increase with time. 4.6 Free Fall: How Far

33. At the end of one second, the rock has fallen 5 meters. At the end of 2 seconds, it has dropped a total distance of 20 meters. At the end of 3 seconds, it has dropped 45 meters altogether. Ugh!!!!!!!!!!!!!!!!!! What does this all mean? 4.6 Free Fall: How Far

34. These distances an object falls form a mathematical pattern: at the end of time t, the object starting from rest falls a distance d. 4.6 Free Fall: How Far

35. Free Fall Distance of an Object Elapsed Time In seconds (s) Distance Fallen Meters (m) Let’s Practice 00 15 220 345 480 5125 t½ gt 2

36. These same principles apply to any accelerating object. When an object’s initial speed is zero and the acceleration a is constant, velocity and distance traveled are: 4.6 Free Fall: How Far

37. think! An apple drops from a tree and hits the ground in one second. What is its speed upon striking the ground? What is its average speed during the one second? How high above ground was the apple when it first dropped? 4.6 Free Fall: How Far

38. Answer: The speed when it strikes the ground is 10 m/s. The average speed was 5 m/s and the apple dropped from a height of 5 meters. 4.6 Free Fall: How Far

39. For a falling object, how does the distance per second change? 4.6 Free Fall: How Far