Kinematics Motion Equations of Motion Constant Acceleration Problem

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

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

Kinematics Motion Equations If the acceleration is constant, we see that these become. Combining these, we find another equation. 3

Kinematics Motion Equations 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 velocity. 4

Kinematics Motion Equations 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. 5

Kinematics Motion Equations 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? 2 6 click the icon to open the worksheet

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

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

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

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

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

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

Kinematics Motion Equations 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. 13

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

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

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

Kinematics Motion Equations 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. 17

Kinematics Motion Equations 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/s 2 downward. The motion diagram for any object in free-fall that starts from rest is the same. 18

Kinematics Motion Equations Free Fall 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. 19

Kinematics Motion Equations Free Fall The motion of a baseball hit at an angle, undergoing free fall is a parabola. 20

Kinematics Motion Equations Free Fall The motion of a rocks thrown from a cliff at different horizontal speeds has some similarities. 21

Kinematics Motion 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 22