Review. acceleration is the rate of change of velocity (how quickly the velocity is changing) For motion in a line. v t

Transcription

1 Accelerated Motion

2 Reiew acceleration is the rate o change o elocity (how quickly the elocity is changing) For motion in a line a i t t

3 When an object is moing in a straight line, a positie acceleration means that the object is speeding up an acceleration o 3 m/s means the object's speed is increasing by 3 m/s or eery second o trael

4 or accelerated motion the position-time graph is a cure Object is speeding up and moing away

5 Accelerated Motion During the 1 st s, object traelled 10m From 1 s to s, moed 30 m From s to 3 s, moed 50 m

6 instantaneous elocity is the elocity o an object at a certain moment Can t ind the slope o a cure or a cured positiontime graph, the instantaneous elocity is the slope o the tangent to the cure

7 What s Happening? Object is slowing down approaching the reerence point

8 What s Happening? Moing away rom you Slowing down

9 What s Happening?

10 the slope o a -t graph will gie the acceleration the area under the -t graph will gie the displacement

11 Area= ½ bh i t since a = and i = 0, = a t 1 t 1 at

12 Check that the area gies units o displacement Area= ½ bh 1 t 1 at I a is in m/s and t is in seconds, Then at =(m/s )s = m since a =

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14 area under the acceleration-time graph will gie the aerage elocity

15 What s Happening?

16 Example Describe the motion Moing away, gradually slowing down time Changes direction and speeds up Goes beyond the reerence point

17 Area under a elocity-time graph is the displacement Area can be negatie

18 For straight line motion, a negatie acceleration means either: the object is moing in the original direction but slowing down OR the object is moing in the opposite direction with an increasing speed

19 Uniorm Accelerated Motion The acceleration magnitude and direction is constant Slope o -t graph is linear

20 Non-uniorm Accelerated Motion Slope o tangent is changing

21 1. What happens at 100 s?. At what time does the object stop?

22 Example Sketch d-t, -t and a-t graphs or an object sliding down a ramp.(no riction)

23 Example A car is moing at 1.0 m/s east when it begins to accelerate at.44 m/s east or 14.0s. Determine its inal elocity. i i i m. s). ( s m /. t a t a t a i i i s m /. s). ( s m /. t a t a t a i i i s m /. s). ( s m /. t a t a t a

24 Example A Starleet Shuttlecrat is moing at 1.67 x 10 4 m/s when it begins to accelerate at -1.9 m/s or 1.0 minutes. Determine its inal speed. a= -1.9 m/s i =1.67x10 4 m/s

25 i i i s m /. s). ( s m /. t a t a t a

26 Example A ball alling down hits the loor at 6.40 m/s and bounces straight up at 4.76 m/s. I the ball is in contact with the loor or s, determine the acceleration o the ball. i = 6.40 m/s down = 4.76 m/s up t = s a a a i t 4.76 m / s ( 6.40 m / s) 0.103s 108 m / s up

27 More! Kinematics Equations i d t 1 d i t a t 1 d t a t i ad

28 Where do the equations 1 d i t a t 1 d t a t come rom?

29 Velocity (m/s) Area = ½ ab 1 t since a = t 1 at Time (s) Area = ab = i t 1 total area = d i t a t

30 Example A plane is moing at 10.0 m/s when it begins to accelerate at 6.00 m/s or 7.00 s. How ar does it moe in this time? 1 d i t a t d=(10.0m/s)(7.00 s) + ½ (6.00 m/s )(7.00 s) d = 17 m

31 Calin and Hobbes are sliding down a hill. I the acceleration is 4.9 m/s and the initial elocity is.6 m/s, determine the magnitude o their displacement ater 6.9 s. Example

32 1 d i t a t Solution d (.6 m / s )(6.9 s ) (4.9 m / s ) 6.9 s 1 1 d m (33.89 m) d m d m

33 Example Slash the cat is running at 1.3 m/s when she speeds up to.1 m/s. As she does, she moes a distance o 7.1 m. For what time was she accelerating? d = i = = t =?

34 i d t Solution 7.1m.1 m / s 1.3 m / s t 7.1m 3.4 m/ s t

35 Solution 7.1m 1.7 m/ s t t 4.s

36 Method : Algebra irst i d t 7.1m.1 m / s 1.3 m / s t d it 14.m d i t 3.4 m/ s t

37 Example The Roadrunner is moing at 10.0 m/s when it begins to speed up. It traels 10 m in 8.00 s. Determine its inal speed. i = 10.0 m/s t = 8.00 s d = 10 m =?

38 i d t i d t i d t / 8.00 i d t m m s s = 0.0 m/s

39 Example Sarah is riding her unicycle at 4.00 m/s when she begins to accelerate at.50 m/s while moing a distance o 00 m. Determine her inal speed. i ad ( 4. 00m/ s) (. 50m/ s )( 00m) 1016m / s = 31.9 m/s

40 A clumsy Star Fleet away team alls o a cli 1 m high and hits the ground in 1.6 s. What is the acceleration o graity on the planet? Practice

41 Solution 1 d i t a t d 1 a t a t d

42 Example Wile E. Coyote is moing at 10.3 m/s when he accelerates to 44.0 m/s in a distance o 30.0 m. Calculate the magnitude o his acceleration i ad a a i d ad i 44. 0m/ s 10. 3m/ s ( 30. 0m)

43 Example A ball is rolled up a long ramp with an initial elocity o 3.00 m/s. The acceleration is.50 m/s down the ramp. a. Calculate the distance the ball will roll up the ramp i = 3.00 m/s a = -.50 m/s d =? = 0 at the highest point

44 ad i ) s m/. ( s m/. s m/ d a d ad i i d = 1.80 m

45 b. Find the magnitude and direction o its elocity ater.15 s. a t a t i a t i i.50 / (.15 ) 3.00 / m s s m s

46 = -.38 m/s =.38 m/s down the ramp

47 Example Ms. Morgan is driing on the Whitemud at 89 km/h. How ar does she trael in 3 minutes, 39 seconds? (The length o her aourite ABBA song.)

48 Solution t = 19 s = 4.7 m/s d = t = 5414 m = 5.4 km

49 Practice P 53:, 4, 6, 8, 10