Chapter 11 The Physics of Motion

Section 11.1 Distance and Displacement Motion is something we are all familiar with, but how do we estimate motion. To describe motion accurately and completely, a frame of reference is necessary. A frame of reference is a system of objects that are not moving with respect to the object in motion.

Section 11.1 Distance and Displacement A frame of reference is necessary for the brain to calculate motion, velocity and distance with any accuracy.

Section 11.1 Distance and Displacement Motion is the movement of an object or objects. Relative motion is the movement of an object in relation to a frame of reference. Example: When driving in a car you are moving as fast as the car but in relationship to the inside of the car you are NOT moving.

Section 11.1 Distance and Displacement The distance traveled is the length of the path between two points along the path the object is taking.

Section 11.1 Distance and Displacement Not all objects move in a straight line. The actual distance traveled is measured as displacement or the length of a straight line between the starting point and the ending point. Example: NASCAR races occur on oval shaped tracks, these races occur in 200 to 500 lap intervals but their displacement is usually very small.

Section 11.1 Distance and Displacement Displacement is an example of a vector. A vector is a quantity that has magnitude and direction. A magnitude can be a size, length or amount.

Section 11.1 Distance and Displacement Displacements are magnitudes of vectors, meaning the distance an object has moved would be the magnitude. These displacements can be combined using vector addition. Vectors can be combined by adding them and subtracting them.

Section 11.1 Distance and Displacement An example of vector addition: You and a friend go for a walk to Burger King which is 4 blocks from your house. You get your food and on the way home stop at another friends house which is 2 blocks from burger king on the way back to your house. How many blocks have you traveled? How far are you from your house.

Section 11.1 Distance and Displacement 4 Blocks 2 Blocks 4 Blocks - 2 Blocks = 2 Blocks

Section 11.1 Distance and Displacement When two or more displacement vectors have different directions they can be combined by graphing. You can combine vectors that travel in different directions by vector addition but this will not give you the distance traveled from start to finish.

Section 11.2 Speed and Velocity Speed is the ratio of the distance an object moves to the amount of time it moves. Speed is most commonly used to describe cars, and the “speed” at which they are traveling. What tool inside a car tells you your speed?

Section 11.2 Speed and Velocity Average speed is a way of looking at the total distance traveled and comparing it to the total time traveled. Average speed = Total distance Total time or v = d t

Section 11.2 Speed and Velocity Calculate the Average Speed: While on vacation, you measure the times and distances traveled. You travel 35 kilometers in 0.4 hours, followed by 53 kilometers in 0.6 hours. What was your average speed?

Section 11.2 Speed and Velocity Instantaneous speed is the rate at which an object is moving at a given moment in time. Next time you are in your parents car watch the speedometer and you will see the change in speed at any given point along the trip.

Section 11.2 Speed and Velocity A distance time graph is a good way to describe motion in relationship to time. The slope of the line on a distance time graph is speed. Remember that the slope of a line on a graph is the rise over the run.

Section 11.2 Speed and Velocity Remember when discussing vectors there must be a direction associated with the measurement. Is speed a vector? Why or why not?

Section 11.2 Speed and Velocity Velocity is a description of both speed and direction of motion, so velocity is the vector related to speed. The longer the velocity vector the faster the speed and the shorter the velocity vector the slower the speed.

Section 11.2 Speed and Velocity The vector arrows can also point in different directions to represent the objects direction. Changes in velocity can occur because of both changes in speed and changes in direction.

Section 11.2 Speed and Velocity Vector addition holds true when it comes to velocity as well. Remember vectors can be combined by addition or subtraction.

Section 11.2 Speed and Velocity An example of vector addition: You and your family want to take your boat out on the Susquehanna River. You launch the boat and start traveling down stream. The river is moving at 5km/h and your boat is moving at a velocity of 12km/h in the same direction. What is your speed relative to the shore line?

Section 11.2 Speed and Velocity 12km/hr + 5km/hr = 17km/hr 5km/hr 12km/hr

Section 11.3 Acceleration Acceleration is the rate at which velocity changes. Acceleration can be described as changes in speed or direction. When you are getting on the interstate with your parents you will notice they speed up to merge with traffic, this is acceleration.

Section 11.3 Acceleration Acceleration is a vector because it describes both a speed and a direction. We commonly think of acceleration as only an increase in speed, it can however also be a decrease in speed.

Section 11.3 Acceleration This can best be described by using the bus ride home most of you will take later today. When the bus slows to a stop you feel yourself move forward this is due to the fact that the buses acceleration is slowing but yours is remaining the same until it is acted on by an outside force. What might some of these forces be?

Section 11.3 Acceleration Another common example of acceleration is free fall, or the movement of an object toward earth due to gravity. When you drop something is it always pushed toward the ground?

Section 11.3 Acceleration Acceleration is not only due to changes in speed as we said. It can be caused by changes in direction. What happens when you are on a roller coaster and you take a sharp turn?

Section 11.3 Acceleration Constant acceleration is a steady change in velocity where the velocity of the object changes by the same amount each second. This ONLY occurs when an object is moving in a straight line.

Section 11.3 Acceleration This is can be seen when you watch the launch of the space shuttle. The acceleration of the shuttle is constant for portions of its assent into space. Why is it not constant the entire time?

Section 11.3 Acceleration You can calculate the acceleration for straight-line motion by dividing the change in velocity by the total time. Acceleration = Change in Velocity Total Time or A= (vf - vi) t

Section 11.3 Acceleration If the resulting acceleration is positive the object is speeding up and if it is negative the object is slowing down.

Section 11.3 Acceleration Calculate the Acceleration: A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball?

Section 11.3 Acceleration Acceleration can be graphed in much the same way that we graphed speed. A distance-time graph however is replaced by a speed-time graph. The slope of the line on the speed-time graph is the acceleration.

Section 11.3 Acceleration A slope which is a straight line is called linear graph. A slope which is arcing or jagged showing a varied or non-constant acceleration is called a non-linear graph.

Section 11.3 Acceleration Instantaneous acceleration is how fast a velocity is changing at a specific instant. Right now you are all sitting in your desks and NOT MOVING!!! What do you think your instantaneous acceleration is at this moment?