1. Physics 151 Week 5 Day 2 Topics –Motion with constant acceleration –Motion Diagrams –Motion Graphs –Area under a curve –Acceleration to velocity –Velocity to position –Constant acceleration equations

2. Slide 2-4 Motion Graph Demonstrations Demo 6: Cart moves toward the motion detector slowing down at a constant rate and then speeds up in the opposite direction Demo 7: Cart moves up inclined ramp, reaches highest point, and rolls back down. Demo 8: The motion detector is placed on the floor. A ball is thrown straight up, reaches its highest point, and comes back down

3. Acceleration Acceleration is: The rate of change of velocity The slope of a velocity- versus-time graph Slide 2-20

4. An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Slide 2-28 Checking Understanding

5. An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which graph best represents the vertical velocity of the arrow as a function of time? Ignore air resistance; the only force acting is gravity. Slide 2-29 Answer

6. Slide 2-34 Velocity to Position: Example 1 Find the position at times t = 1, 2, 3, 4, and 5 seconds. Assume x (t = 0 sec) = 0 m. What is the displacement of the object between t = 1s and t = 3 s?

7. Slide 2-34 Velocity to Position: Example 2 Describe in words the motion of the object whose velocity graph is given below. What is happening at t = 2 s? Draw a motion diagram of the objects motion. Draw the corresponding position vs. time graph. Assume initial position is 5 m. Give an example of an object that would move this way

8. Slide 2-34 Start your engine (velocity and acceleration) On the on ramp to Interstate 25 a car accelerates at 7 m/s 2 from rest. What is the car's velocity at 1 second after it starts from rest? 2 seconds? 3 seconds? 4 seconds? Express your reasoning in words.

9. Slide 2-4 Velocity Graph => Acceleration Graph

10. Slide 2-4  x = area under v x vs. t graph

11. Slide 2-4  v x = area under a x vs. t graph

12. Slide 2-4 General Motion Model Graph Relationships

13. Slide 2-4 Constant Acceleration Equations Area 1 Area 2

14. Slide 2-4 Constant Acceleration Equations (Equation 3)

15. Slide 2-4 Constant Acceleration Equations (Equation 3) Unit Check => ???

16. Pictorial Diagrams

17. Pictorial Diagram Example 1

18. Pictorial Diagram Example 2

19. Slide 2-4 The Sprinter A sprinter accelerates at 2.5 m/s^2 until reaching his top speed of 15 m/s. He then continues to run at top speed. How long does it take him to run the 100 m dash?

20. Slide 2-4 Down and Up A ball is released on the left side at a height of 1 m on a frictionless 30 degree slope, |a| = 5 m/s 2. At the bottom, it turns smoothly onto a 60 degree slope going back up, |a| = 8.66 m/s 2. What maximum height does it reach on the right side?