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Distance

Distance. The actual path length traveled by an object in motion A scalar quantity Positive values only. Displacement . Straight line distance from the initial position to the final position (change in position) Vector quantity Can be positive or negative. Displacement.

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Distance

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  1. Distance • The actual path length traveled by an object in motion • A scalar quantity • Positive values only

  2. Displacement  • Straight line distance from the initial position to the final position (change in position) • Vector quantity • Can be positive or negative

  3. Displacement • What is the displacement (in cm) for the objects shown? • Answer: 70 cm • Answer: -60 cm

  4. Displacement - Sign Conventions • Right (or east) ---> + • Left (or west) ---> – • Up (or north) ----> + • Down (or south) ---> –

  5. Average Velocity • Average velocity is displacement divided by the time interval. • The units can be determined from the equation. • SI Units: m/s • Other Possible Units: mi/h, km/h, cm/year

  6. 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

  7. 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.

  8. 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

  9. What do you think? • Which of the following cars is accelerating? • A car shortly after a stoplight turns green • A car approaching a red light • A car with the cruise control set at 80 km/h • A car turning a curve at a constant speed

  10. Acceleration • Rate of change in velocity • What are the units? • SI Units: (m/s)/s or m/s2 • Other Units: (km/h)/s or (mi/h)/s • Acceleration = 0 implies a constant velocity (or rest)

  11. Acceleration Click below to watch the Visual Concept. Visual Concept

  12. Classroom Practice Problem • Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s. • Answer: 9.3 m/s2 downward

  13. Useful Equations 1. 2. 3. 4. 5.

  14. Classroom Practice Problems • A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval? • Answer: 84 m • An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing? • Answer: -18.0 m/s2

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