Constant Acceleration

1. Equations of Motion Constant Acceleration Constant Acceleration Problem Solving Centripetal and Tangential Acceleration Free-Fall Motion

2. Motion can be determined by using a few simple equations. The relationships between velocity and position are… The relationships between acceleration and velocity are…

3. Here are some examples of how the equations are used. Given an x-component of position What is the x-component of the velocity at time t = 5s.

4. Here are some examples of how the equations are used. Given an x-component of velocity How far does the object move between t = 5s and t = 10s.

5. Here are some examples of how the equations are used. Given an x-component of velocity What is the x-component of the acceleration at time t = 5s.

6. If we have a constant acceleration, then the equations become algebraic.

7. In simpler notation, we see that these become. Combining these, we find another equation.

8. We can use these three equations to solve for any motion involving constant acceleration. This equation relates velocity and time. This equation relates position and time. This equation relates position and velocity.

9. If we are only dealing with one vector component, then the equations become simple. Let’s just look at the x-component The y-component and z-component equations are similar.

10. 2 Now let’s see how we use them. Example: Two race cars are moving on a racetrack. The lead car is ahead by 10 m. Both cars are currently moving at 100 km/hr. If the second car accelerates at 10 m/s2, how long will it take to reach the lead car? click the icon to open the worksheet

11. 2 Now let’s see how we use them.

12. 2 Now let’s see how we use them.

13. 2 Now let’s see how we use them.

14. 2 Now let’s see how we use them.

15. 2 Now let’s see how we use them.

16. 2 Now let’s see how we use them.

17. What Happened to Centrifugal Force? There is no such thing as centrifugal force. So where did it come from? A mistaken assumption is made that the forces on particles moving in a circle with constant speed have no forces acting on them. Why is this false? Acceleration comes from changes in velocity (direction, not just speed). Circular motion requires acceleration and thus requires force.

18. What Happened to Centrifugal Force? The myth starts from the mistaken idea that there is no acceleration and therefore the total force is zero.

19. What Happened to Centrifugal Force? The fact is that velocity is changing and the acceleration is the centripetal acceleration. The force is NOT zero!!!!

20. Centripetal vs. Tangential Acceleration Centripetal acceleration causes a particle to change its direction. It points toward the center of the circle

21. Centripetal vs. Tangential Acceleration Tangential acceleration causes a particle to change its speed. It points along the tangent to the line of motion.

22. Centripetal vs. Tangential Acceleration You can also have a combination of both.

23. Centripetal vs. Tangential Acceleration You can also have a combination of both.

24. Free Fall Any particle, subject only to the force of gravity is in free-fall. If an object is in free-fall and we define the positive y-axis as upward, then its acceleration is always given by where g is the acceleration due to gravity and has a value of 9.81 m/s2 near the surface of the earth. Note that the acceleration parallel to the earth’s surface is zero.

25. Free Fall Particle’s in free fall are subject only to the force of gravity. Every particle in free-fall has an acceleration of 9.81 m/s2 downward. The motion diagram for any object in free-fall that starts from rest is the same.

26. Free Fall • For particle’s that do not start at rest… • The vertical acceleration is 9.81 m/s2 downward. • The horizontal acceleration is zero. (The horizontal velocity is constant.) • In other words, objects move in a very predictable way. • But then, you already know this.

27. Free Fall The motion of a baseball hit at an angle, undergoing free fall is a parabola.

28. Free Fall The motion of a rocks thrown from a cliff at different horizontal speeds has some similarities.

29. Equations In free fall, the vertical position, velocity and acceleration are related by the equations the horizontal position, velocity and acceleration are related by the equation Note that we can write the components of the initial velocity as

30. Sample Problem A monkey is hanging from a tree. A zookeeper wishes to shoot the monkey with a tranquilizer dart. When the zookeeper shoots, he knows that the monkey will hear the shot and let go of the branch trying to avoid the dart. Should the zookeeper aim above, below or directly at the monkey?

31. Sample Problem Bailey D. Wonderdog snatches the homerun away from Dr. Mike. This is the one we went over in class. http://web.nmsu.edu/~mdeanton/Fundamentals/Kinematics/Constant_Acceleration_and_Circular_Motion/Example%201.pdf

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