# Motion in One DimensionSection 1 Preview Section 1 Displacement and VelocityDisplacement and Velocity Section 2 AccelerationAcceleration Section 3 Falling.

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Motion in One DimensionSection 1 Preview Section 1 Displacement and VelocityDisplacement and Velocity Section 2 AccelerationAcceleration Section 3 Falling ObjectsFalling Objects

Motion in One DimensionSection 1 Preview Section 1 Displacement and VelocityDisplacement and Velocity One Dimensional Motion Displacement vs. DistanceDisplacement Average Velocity Velocity and Speed Interpreting Velocity Graphically

Motion in One DimensionSection 1 What do you think? Is the book on your instructor’s desk in motion? –Explain your answer.

Motion in One DimensionSection 1 One-Dimensional Motion and Distance Motion in one dimension refers to straight-line motion (Linear) Example: train traveling on a straight track

Motion in One DimensionSection 1 Frame of Reference Motion –a change in position Frame of reference –A point against which position is measured Example: A train traveling between stations –It is in motion when measured against the track. –It is stationary when measured against a seat.

Motion in One DimensionSection 1 Displacement (  x)  Straight line distance from the initial position to the final position (change in position) Can be positive or negative Keep in mind that distance is the total length of the path traveled by an object 5 m 7 m 5 m = 17 m

Motion in One DimensionSection 1 Think: How is it possible for a car to travel a distance of 5 miles, and have a displacement is equal to zero. Drive around a very long block and return to the starting position. Back out of your garage, drive 5 miles, and return to your garage.

Motion in One DimensionSection 1 Positive and Negative Displacements

Motion in One DimensionSection 1 Displacement What is the displacement for the objects shown? Answer: 70.0 cm Answer: -60.0 cm

Motion in One DimensionSection 1 Displacement - Sign Conventions Right (or east) ---> + Left (or west) ---> – Up (or north) ----> + Down (or south) ---> –

Motion in One DimensionSection 1 Average Velocity Average velocity is total displacement divided by the time interval during which the displacement occurred.

Motion in One DimensionSection 1 Section 1 Displacement and Velocity Chapter 2 Average Velocity The units can be determined from the equation. –SI Units: meters per second or m/s –Other Possible Units: mi/h, km/h, cm/year Velocity can be negative or positive; the sign represents a direction (sign based on sign of displacement) right/east positive left/west negative

Motion in One DimensionSection 1 Classroom Practice Problems A car travels 36 km to the north in 30.0 min. Find the average velocity in km/min and in km/h. –Answer: 1.2 km/min to the north or 72 km/h to the north A car travels 100.0 km to the east. If the first half of the distance is driven at 50.0 km/h and the second half at a 100.0 km/h, what is the average velocity? –Answer: 66.7 km/h to the east

Motion in One DimensionSection 1 Constant Velocity Object maintains the same speed in the same direction Example: Car travels at 35 km/h due east

Motion in One DimensionSection 1 Instantaneous Velocity Velocity at a single instant of time –Speedometers in cars measure instantaneous speed. Determined by finding the slope at a single point (the slope of the tangent) What is the slope of the tangent line at t = 3.0 s? –Answer: approximately 12 m/s What is the instantaneous velocity at t = 3.0 s? –Answer: approximately 12 m/s

Motion in One DimensionSection 1 Speed Speed does not include direction while velocity does. Speed uses distance rather than displacement. In a round trip, the average velocity is zero but the average speed is not zero.

Motion in One DimensionSection 1 Velocity and Speed Velocity describes motion with both a direction and a numerical value (a magnitude). Speed has no direction, only magnitude.

Motion in One DimensionSection 1 Graphing Motion Position (distance) vs. Time Graphs At rest, no change in position

Motion in One DimensionSection 1 Graphing Motion Position (distance) vs. Time Graphs Yellow line (constant speed of 3 m/s) Blue line (constant speed of 1 m/s) The velocity of the object can be calculated by evaluating the slope of each line, or one point along each line. The objects shown by the yellow and blue lines are covering equal amounts of distance in equal amounts of time.

Motion in One DimensionSection 1 Graphing Motion Position (distance) vs. Time Graphs Changing distance over time or acceleration. The object represented by the yellow line is covering a greater amount of distance with each unit of time that passes. (it is speeding up)

Motion in One DimensionSection 1 Graphing Motion (position vs. time) What type of motion does this graph show? –Answer: Constant speed (straight line) What is the slope of this line? –Answer: 1 m/s What is the average velocity? –Answer: 1 m/s

Motion in One DimensionSection 1 Graphing Motion Describe the motion of each object. Answers –Object 1: constant velocity to the right or upward –Object 2: constant velocity of zero (at rest) –Object 3: constant velocity to the left or downward

Motion in One DimensionSection 1 Now what do you think? Is the book on your instructor’s desk in motion? –How does your answer depend on the frame of reference? What are some common terms used to describe the motion of objects?

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