Chapter 3: Introduction to Motion

Transcription

1 Chapter 3: Introduction to Motion Motion... Particle Models Vectors vs. Scalars Position, Displacement and Distance Velocity vs. Speed Instantaneous vs. Average Acceleration

2 start time Particle motion diagrams direction of motion start time

3 . A B C 0 5 meters 12 meters 12 5 position ( m) 0 straight 0 time Time The motion of the object above shown on the number line is "modeled" on this position time graph A B C time Notice how the upward tipped curve corresponds with speeding up and the downward tipped curve corresponds with slowing down

4 Position: the location of an object with respect to a clear point of reference includes both a statement of distance and a direction this makes position a VECTOR quantity (has both magnitude and direction) mks units: meters (m) Distance: is simply how far apart two points are or a statement of total length travelled without regard to direction. distance is a SCALAR quantity( only has magnitude) distance also has mks units of meters (m) Displacement: The overall vector change in position of an object d = d 2 d 1 Displacement is a VECTOR displacement is also measured in meters (mks)

5 Rhinebeck Milan Pine 10 km 12 km Plains X X X start route If Mr. B leaves Rhinebeck and drives east to Pine Plains, then he turns around and drives west to Milan, 22 km End 12 km Find the total distance he drove: 22 km + 12 km = 34 km Find his overall displacement 10 km east

6 meters start position end position Displacement = d = d 2 d 1

7 meters end position start position Displacement = d = d 2 d 1

8 meters start position end position Displacement = d = d 2 d 1

9 Average Velocity v = d t is the overall time rate at which a displacement occurred. Vector! mks units Average Speed = Example: Scalar! Total Distance Time elapsed Mr. Boucher, starting in Rhinebeck drives to 15 km West to Kingston, then turns around and drives 50. km East to Pine Plains. The whole excursion takes exactly one hour. Displacement start x x 15 km West Kingston Rhinebeck 50. km East end x Pine Plains Average Velocity v d = = t his overall displacement = 50 km 15 km = 35 km East 35 km East 1.0 hrs = 35 km/hr, East Average Speed Average Speed = Total Distance Time elapsed = 65 km 1.0 hrs = 65 km/hr

10 Vectors vs. Scalars Vectors are physical quantities that possess both Magnitude (size) and Direction Scalars are physical quantities that do not possess direction qualities. ( or direction is excluded by definition) What do vectors have that scalars don't? DIRECTION

11 Scalars Vectors mass Volume Distance density Energy temperature Speed time Displacement Acceleration Force Position Velocity

12 Average vs Instantaneous Average speed is determined by taking the distance covered and dividing it by the time elapsed you can find average speed by using your car's odometer( or tripometer) and dividing by the time elapsed. Instantaneous speed is determined by finding your speed at a particular instant. Speedometers indicate the instantaneous speed of our cars. We will infer average and instantaneous speed from position vs. time graphs in Chapter 5 This graph shows an object moving forward (in the positive direction) with changing speed We can infer it had low but increasing velocity for the first ~ 15 seconds because the curve's steepness (slope) is increasing. We can also correctly infer that its velocity was constant between ~20 and ~35 seconds because the curve straightens into a line Finally, we can infer the average velocity by taking the slope of the line that connects the start point to the end point on the graph. In this case, it's about: Avg vel = 280 meters 48 sec = ~ 5.8 m/s

13 Acceleration acceleration is the time rate of change of velocity It is a vector! average = acceleration a = v t units: m/s/s say: meters per second per second equivalent to: m/s 2