Physics - Motion Module 6 Motion • Motion is a change in position or direction, usually over a certain amount time • When you say that something has moved, you are describing motion. • In describing motion, you are comparing it with some frame of reference. Relative Motion – Movement in relation to a frame of reference • When describing something that is moving, you are comparing it with something that is assumed to be stationary (not moving). • The frame of reference is the background or object that is used for comparison. The frame of reference is that stationary “something.” • A frame of reference refers to using a reference point to detect motion • Ex: You are on a train that just left the platform. • The people standing on the platform see you moving away. (earth) • The person sitting next to you does not see you moving. (train) Frame of Reference cont’d • Frame of reference depends on the type of movement and position from which you are observing. • An audience watching a car race may be sitting still but appear blurry in an image, knowing that cars tend to move faster than people we view the image as if the car is moving, not the audience • In this example assume the background is stationary knowledge about this situationbecause of prior • Earth is the most commonly used frame of reference. Frame of Reference cont’d • In physics motion is always measured relative to something else. That “something else” is usually called a reference point. • Reference point – a point against which direction is measured • An object’s position is its location within the frame of reference and the motion of the object depends of the frame of reference. Measuring Distance • Distance is the length of a path between two points (Distance does not need a reference point and does not include direction) • Remember that the SI unit for distance (length) is the meter (m). Centimeters (cm) is used for measuring shorter distances, and kilometers (km) is used to measure longer distances Measuring distance • Measuring distance alone cannot give us the final position of a person or object that has traveled. • To find the final position of a person or object, take the distance traveled and direction of motion from the starting point to the ending point in a straight line • This change in the position of an object is called its displacement. • Displacement – The distance an object travels plus the direction from the starting point to ending point in a straight line. Distance versus Displacement Distance vs. Displacement • You drive the path in red, and your odometer goes up by 8 miles (your distance). • Your displacement is the shorter direct distance from start to stop (green arrow). • What if you drove in a circle? What would your displacement be? start stop Physical Quantities • A physical quantity such as displacement, tells us two types of information. It tells us magnitude (which means size or quantity) and the direction. • Physical quantities that carry information concerning direction are called vector quantities. • Vector quantity – a physical measurement that contains both magnitude (number and directional information. • Physical quantities that contain only information about magnitude are called scalar quantities • Scalar quantity – a physical measurement that contains only magnitude (number) and does not contain directional information Displacement Along a Straight Line Displacement along a Straight Line Physical Quantities Distance versus Displacement – baseball example • If you hit a home run in baseball, you would run from home plate, to each of the bases (1 through 3) and then back to home plate. If there is a distance of 30 meters between each of the bases, what is the total distance you run? What is your displacement? • Remember: • Distance is the length of the path taken from point A to point B. • Displacement is the distance and direction from point A (beginning point) to point B (end point) in a straight line. Displacement that is not along a straight line • When two or more vectors have different directions, they may be combined using graphing. • Example: • A person walking to a store walked 1 block east, then 1 block north, then they turned and walked two blocks east, and then finally 3 blocks north. What is the distance they traveled? What is their displacement? • To find the total distance you add the magnitudes of each vector together. • So the person walked a total distance of 7 blocks to reach their destination • To find the displacement of the person walking to the store you need to find the distance and direction from the starting point to the ending point in a straight line. • This can be accomplished by using the graph to the right. • Draw a straight line connecting the starting and end point together. Measure the length of the line and compare it to the scale of on block on your graph. • Doing so, you would see that the line is 5 blocks in length. So the displacement of the person traveling to the store is 5 blocks northeast. Speed and Velocity • If an object is in motion, its position is changing. Over time, that will result in a distance over which the object travels. This is called the object’s speed. • An objects velocity is its speed including information about its direction. • Speed tells you how quickly an object moves in relation to a reference point. • Velocity tells you how quickly and in what direction the object is moving in relation to a reference point Speed vs. Velocity • Speed is a scalar quantity (it does not consider direction) Ex: v = 20 mph • Speed is often the magnitude of velocity. • Velocity is a vector quantity (it considers both speed and direction). Ex: v = 20 mph at 15 south of west Speed • Speed is the rate at which an object moves. • The faster a runner’s rate of motion, the faster the runner’s speed. • Speed = distance/time • Units = m/s Speed • Speed is described in units of distance and time. • The SI units for speed are meters per second (m/s) –other common units km/h, ft/s, mi/h • Example) In a race, the runners have to move or change positions to get to the finish line in a certain amount of time. • To describe speed accurately you need to know: • distance traveled (meters – m) • how long it took to go that distance (seconds – s) You need to know the equations – this chart is helpful Average speed versus instantaneous speed • Average speed – the ratio of the total distance traveled to the total time of the trip. • When you ride your bike you likely do not travel at the same speed the entire time. You speed up when you go down hills, you might take breaks, you slow down going up hills. This means that your speed is not constant. Therefore how fast something moves for an entire trip is considered an average. It is an average of all the different speeds you traveled during your bike trip. • Instantaneous speed – the rate at which an object is moving at a given moment in time. • If, for example, your parents are driving on a highway and the speed limit changes they need to know how fast they are going right at that instant. The speedometers in cars provide such information, and therefore tell a driver their instantaneous speed. Average Speed • Not all objects move at constant speeds. • The average speed also uses the formula speed = total distance/ total time • Going to Columbus, Georgia, you change speeds during the drive many times. So over all you travel at an average speed. Constant Speed • Objects in motion that maintain the same speed, are moving at a constant speed. • Total distance divided by total time give speed at any point in time. • A Graph of speed will be a straight line if speed is constant Graphing Speed Graphing Speed cont’d Average Speed Example Problem • Jack is traveling on a bike from home to school. Using a graph of position/distance (y-axis) and time in minutes (x-axis) we can examine his speed throughout the route he took. • Can you determine the Jack’s average speed for his trip to school? Problem • At what speed did a plane fly if it traveled 1760 meters in 8 seconds? • Steps: • 1 – Write a formula • 2 – Substitute given numbers and units • 3 – Solve for the unknown Speed, Velocity, & Acceleration • Speed (v) – how fast you go • Velocity (v) – how fast and which way (direction); the rate at which displacement changes • Acceleration (a) – how fast you speed up, slow down, or change direction; the rate at which velocity changes Velocity • Velocity is speed in a given direction. It is also determined by using the distance from the starting position to the ending position, rather than the distance of the path taken. • A runner moves eastward at 10m/s. • speed is 10m/s • velocity is 10m/s east • Velocity is very important for airplane pilots, weather forecasters, and anyone driving from one place to another. Velocity • When objects are moving in the same direction, we can get their relative speed by subtracting their individual speeds (relative speed = speed of object 1 – speed of object 2) • When objects travel in opposite directions, we can get their relative speed by adding their individual speeds. (relative speed = speed of object 1 + speed of object 2) • Once you determine the relative speed of an object or objects you can turn that into velocity by adding whether they are moving away from or toward eachother. Acceleration • The rate of change in an object’s velocity is known as acceleration. • If something is accelerating, it is doing one of the following: • speeding up • slowing down • changing directions Keep in mind: • If an object speed up, the velocity obviously changes. • If an object slows down, the velocity obviously changes. • Finally, if an object changes direction, the velocity changes. • When an object is in motion and its velocity changes, we say that is acceleration. • Acceleration can increase • Acceleration can decrease Acceleration Speed units = Time units Speed units Time units = • Final = ending velocity • Original = starting velocity • It tells how fast something is moving and gives direction. • Used when there are changes in velocity. • Units • Common: m/s2 • Distance unit divided by time unit squared m s s 1 = m s m s s x 1 m = 2 s s Problem • A roller coaster’s velocity at the top of a hill is 10m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the roller coaster? • Steps: • 1 – write the formula • 2 – substitute given numbers and units • 3 – solve for the unknown Decreasing acceleration • When there is a decrease in velocity, the value of acceleration is negative. • Negative acceleration = decreasing acceleration • Positive acceleration = increasing acceleration • Distance – time graphs for acceleration are always a curve. Graphing velocity and acceleration The slope of an distance versus time graph is velocity The slope of a velocity/speed versus time graph is acceleration The slope of an acceleration versus time graph is the rate of change of acceleration (jerk) Circular Motion • In circular motion, the velocity is continuously changing because direction is continuously changing. • An object in circular motion is accelerating even though its speed may be constant. • Ex of acceleration in a circular motion: Ferris wheel, carousel Practice, Practice, Practice • While traveling on vacation, you measure the time and distances you traveled. You travel 88 kilometers in 1.0 hour. What is your average speed? • Remember: speed (v) = distance time Practice, Practice, Practice 1. A car travels 78 miles down the highway. It takes the car 1.2 hours to travel that far. What is the average speed of the car? • Total distance: _______ • Total time: __________ • Average speed: ___?___ 2. Write out the equation substituting the number from the list above and solve Practice, Practice, Practice 1. A person on a bike travels 5 miles down the highway. It takes the biker 4 hours to travel that far. What is the average speed of the biker? • Total distance: _______ • Total time: __________ • Average speed: ___?___ 2. Write out the equation substituting the number from the list above and solve Practice, Practice, Practice 1. Two cars are traveling down a road. The first car is traveling north at 55 mi/h, and the second car is a few hundred yards behind, traveling north at 45 mi/h. What is their relative velocity? • Velocity of car 1: _______ • Velocity of car 2: __________ • Relative velocity: ___?___ For objects traveling in the same direction Relative speed = speed of object 1 – speed of object 2 2. Write out the equation substituting the number from the list above and solve. (remember velocity is speed plus direction; relative velocity is speed plus whether objects are moving towards or away from each other) Practice, Practice, Practice 1. Two cars are traveling down a road. The first car is traveling north at 55 mi/h, and the second car is a few hundred yards south, traveling south at 45 mi/h. What is their relative velocity? • Velocity of car 1: _______ • Velocity of car 2: __________ • Relative velocity: ___?___ For objects traveling in opposite directions Relative speed = speed of object 1 + speed of object 2 2. Write out the equation substituting the number from the list above and solve. (remember velocity is speed plus direction; relative velocity is speed plus whether objects are moving towards or away from each other) Practice, Practice, Practice 1. Suppose a ball is falling. A person with a radar gun measures its velocity to be 2.0 ft/s straight down. Just 30 seconds later, he measures the velocity again and finds that it is 11.6 ft/s straight down. What is the balls acceleration? • • • • Initial velocity: _______ Final velocity: ________ Time: _______________ Relative velocity: ___?___ 2. Write out the equation substituting the number from the list above and solve. Practice, Practice, Practice 1. A bicyclist is traveling down a road at 18 ft/s to the east. The cyclist sees an obstacle in the road ahead, so he hits the brakes. In 1.8 seconds, the cyclist has come to a complete stop. What is the cyclist’s acceleration? • • • • Initial velocity: _______ Final velocity: ________ Time: _______________ Relative velocity: ___?___ 2. Write out the equation substituting the number from the list above and solve.
