THE STUDY OF MOTION Where are you? Where are you going? How fast are you moving?

Resources- Science Voyages, Level Blue, Glencoe/McGraw-Hill, 2000 Science Interactions, Course 1, Glencoe, 1993 Motion, Forces, and Energy, Prentice Hall, 1993

This is your vocabulary- position reference point motion distance SI meter unit time speed speedometer odometer displacement velocity relative frame of reference average constant instantaneous

These are your formulas- Speed = Distance Time Velocity = Displacement Time

So, where are you? You and your friend agree to meet for a movie tonight. You decide to get together 100 feet south of the Bayside Supermarket in 30 minutes. Where you will meet is the position as described by a reference point. A reference point is an object that does not move. To describe a position, you must define three things: the reference point, how far from the reference point the position is and in what direction. The time you will meet is measured with a clock. Time is defined as the interval between two events (when you make the decision to meet and when you meet). Over the years, time has been measured with sundials, hour glasses, watches, and the most accurate clock, the atomic clock.

While you were walking to meet your friend, you were in motion. Changing position creates motion. You have gone a distance, and time has passed while you were changing your position.

As you walk to meet your friend, you change your position with every step you take. Distance is how far you travel along a path while you change your position. Distance is measured in SI units. This is a system of measurement that scientists all over the world use so they can communicate information clearly. SI stands for the International System of Units called the metric system, a system based on the number ten. The basic unit of length is the meter (m).

Let’s talk displacement- Have you ever ridden a roller coaster? You twist and turn for three or four minutes, but you get on and off at the same place. Even with all the turns, you really haven’t gone anywhere at all. Displacement is the change in position of an object. If you end up where you started, your displacement is zero. Displacement is described by both a length and a direction. Distance is described only by length. To say that you live 6 km from the amusement park isn’t very helpful unless you state in which direction (6 km south).

Does it sound like distance and displacement are the same thing? You live 10 km away from school. There is a heavy snow. It took you 5 hours to walk to school. So, what is the distance you traveled? What is your displacement? Well, if you walked in a straight line, through houses, trees, and fences, it would be 10 km. But if one connected all your footprints and measured the distance, it was actually 15 km. The distance is 15 km. Your displacement is 10 km in the direction of the school.

Let’s work a problem or two- Mrs. Heyden travels 22 miles each day to get to school. If she could fly in a straight line, she would only have to travel 15 miles toward the east. Which of these values is the distance she travels and which is her displacement? The 22 miles is the distance she travels and the 15 miles east is her displacement. Click here for the answer. A girl walks 2 km west, she turns and walks 3 km east. What distance does she walk? What is her displacement? The distance she walked 5 km. Her displacement is 1 km east. Click here for the answer.

To be able to meet your friend on schedule, you had to go a distance in a certain time. Speed is the distance traveled by an object during a given time interval (distance divided by time). You stop for a few minutes to watch a ball game at a local park, hurry to cross the street, and rush to get there on time. You do not maintain a constant speed. Even if your speed isn’t constant, you can find your average speed by using this equation--- Speed = Time = Distance O.K. Just how fast are you moving?

v = 2 km/min t = 4 min d = 8 km What else can we calculate using the formula for speed? Suppose you were given the speed and the time. Could you determine the distance? This time you know the distance and the speed. Can you find out how long it took for the cheetah to go the distance? Yes. d = v t Yes. t = d / v

Instantaneous speed- Instantaneous speed is the rate of motion at any given instant. What does that mean? The picture at the right gives you the speed of the runner at the instant the picture was taken. 8.5 meters/second The speedometer in your car gives you a reading of instantaneous speed. While the speedometer is showing the speed at any given moment, the odometer shows you how far you have gone. An odometer measures distance

average speed = total distance time interval A cheetah can maintain a constant speed for short periods of time. Its speed is the same at all times during its motion. In 4 minutes, the cheetah traveled 8 km. speed = 8 km 4 min = 2 km/min Most objects do not move at constant speeds for very long. Dividing the total distance by the total time does not tell you the speed for every point of the journey. Instead it gives you the average speed. The rabbit had a burst of speed during the second minute. What is going on between the 3 rd and 4 th minutes? Time Answer The rabbit is not moving. Time passes but no distance is covered. Di sta nc e

500 km Distance = speed x time Let’s work a problem or three- A car travels 240 km in 3 hours. What is the speed of the car during that time? 80 km/hr Speed = Distance/Time Check for your answer  A ship can travel at a speed of 50 km/hour. How far will it have traveled if it sails for 10 hours? (Something different here!) Check for your answer  2 hrs time = distance/speed A friend lives 4 km away. If he walks at a speed of 2 km/hour, how long will it take him to travel that distance? (Be careful! You will need to use a different version of the formula to solve this one.)

Velocity When you know the speed and direction of an object’s motion, you know the velocity of the object. For example, the meteorologist (one who studies the weather) gives the velocity of the wind. The wind is out of the southwest at 10 km/hr. Velocity is the displacement of an object divided by time.

The formula for velocity is- Velocity = Displacement Time = In the formula, v stands for average velocity and d for displacement. Time is t. v = d t

In the previous example, your speed would be 3 km/hr, but your velocity would be 2 km/hr in the direction of the school. If you walk back home, your displacement is zero, and your velocity is 0 km/hr. Well, just think of it, all the years you walked to school and back home your displacement and velocity were both zero! Click here to view how to do these problems. How about speed and velocity? Are they the same thing? 15 km/5 hr = 3 km/hr (speed) 10 km/5 hr = 2 km/hr in the direction of the school (velocity)

Let’s work a problem or two- An airplane is flying in a straight line from Bridgeport, WV, to Washington, DC., a displacement of 330 km east. The trip takes 1.5 hours. What is the airplane’s velocity? The total displacement divided by total time is a velocity of 220 km/hr east. Click here for the answer. A ball is thrown straight up in the air and is caught at the same height from which it was launched. If it reached a height of 2 m and was in the air for a total of 2 seconds what was its speed? What was its velocity? The ball's speed was 1 m/s (s = 2 m/2 s = 1 m/s). The ball's velocity was 0 m/s. (Displacement = 0 m) Click here for the answer.

Frame of reference- When you describe something that is moving, you are comparing it with something that stationary or not moving. This stationary object is your frame of reference. Think about an astronaut on a space walk. If you are the astronaut, the shuttle is your frame of reference (your relative velocity to the shuttle is zero). But, if you are on the ground, you would describe both the astronaut and the shuttle having a velocity of 40,000 km/hr. The Earth is your frame of reference.

Frame of reference- POP Quiz You, sitting at your desk, are traveling at which of the following speeds? A) 0 mi/hr B) 1,036 mi/hr C) 66,705 mi/hr D) All of the above A) 0 mi/hr B) 1,036 mi/hr C) 66,705 mi/hr D) All of the above You, sitting at your desk, are traveling about the center of the earth at approximately 1,036 mph! You, sitting at your desk on the earth, are traveling about the Sun at approximately 66,705 mph! You, sitting at your desk, are traveling 0 mph relative to the classroom (and earth)!

Combining velocities- Suppose you are swimming downstream at 10 km/hr. You are actually going faster. How? The water is moving at 10 km/hr. Since you are swimming downstream, both you and the river are going in the same direction. The velocities combine (add). You are moving at 20 km/hr. What would happen if you were swimming upstream against the flow of water? Velocities must be in the same direction to add them. You must subtract when combining velocities in opposite directions. You would be swimming at 0 km/hr or simply going nowhere! 10 km/hr downstream – 10 km/hr upstream = 0 km/hr Click here for the answer.