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

2. Kinematics Motion Equations 2 Motion can be determined by using a few simple equations. The relationships between velocity and position are (if velocity is constant) The relationships between acceleration and velocity are (if acceleration is constant)

3. Kinematics Motion Equations 3 For constant acceleration, we always have three valid equations. Combining these, we find another equation.

4. Kinematics Motion Equations 4 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.

5. Kinematics Motion Equations 5 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.

6. Kinematics Motion Equations 6 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/s 2, how long will it take to reach the lead car? click the icon to open the worksheet 2

7. Kinematics Motion Equations 7 Now let’s see how we use them. 2

8. Kinematics Motion Equations 8 Now let’s see how we use them. 2

9. Kinematics Motion Equations 9 Now let’s see how we use them. 2

10. Kinematics Motion Equations 10 Now let’s see how we use them. 2

11. Kinematics Motion Equations 11 Now let’s see how we use them. 2

12. Kinematics Motion Equations 12 Now let’s see how we use them. 2

13. Kinematics Motion Equations 13 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.

14. Kinematics Motion Equations 14 What Happened to Centrifugal Force? The myth starts from the mistaken idea that there is no acceleration and therefore the total force is zero.

15. Kinematics Motion Equations 15 What Happened to Centrifugal Force? The fact is that velocity is changing and the acceleration is the centripetal acceleration. The force is NOT zero!!!!

16. Kinematics Motion Equations 16 Centripetal vs. Tangential Acceleration Centripetal acceleration causes a particle to change its direction. It points toward the center of the circle

17. Kinematics Motion Equations 17 Centripetal vs. Tangential Acceleration Tangential acceleration causes a particle to change its speed. It points along the tangent to the line of motion.

18. Kinematics Motion Equations 18 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/s 2 near the surface of the earth. Note that the acceleration parallel to the earth’s surface is zero.

19. Kinematics Motion Equations 19 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/s 2 downward. Free Fall The motion diagram for any object in free-fall that starts from rest is the same.

20. Kinematics Motion Equations 20 For particle’s that do not start at rest… 1.The vertical acceleration is 9.81 m/s 2 downward. 2.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. Free Fall

21. Kinematics Motion Equations 21 The motion of a baseball hit at an angle, undergoing free fall is a parabola. Free Fall

22. Kinematics Motion Equations 22 The motion of a rocks thrown from a cliff at different horizontal speeds has some similarities. Free Fall

23. Kinematics Motion Equations 23 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