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Chapter 3 Describing Motion

Chapter 3 Describing Motion. Scalar A quantity that has only magnitude. Time (t) Mass (m) Distance (d) Temperature (T) Speed (s). Chapter 3 Describing Motion. Vector A quantity with magnitude and direction Velocity ( V ) Displacement ( D ) Force ( N ) Weight ( N ).

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Chapter 3 Describing Motion

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  1. Chapter 3Describing Motion Scalar A quantity that has only magnitude. • Time (t) • Mass (m) • Distance (d) • Temperature (T) • Speed (s)

  2. Chapter 3 Describing Motion Vector A quantity with magnitude and direction • Velocity (V) • Displacement (D) • Force (N) • Weight (N)

  3. Chapter 3Describing Motion • Displacement The distance and direction between two positions. • Average Velocity The ratio of the change in position to the time interval during which the change occurred. • Average Speed The ratio of the total distance traveled to the total time interval.

  4. Chapter 3Describing Motion • Average Velocity • Displacement

  5. Chapter 3Describing Motion • Instantaneous velocity The speed and direction of an object at a particular time. The symbol for instantaneous velocity is represented by the symbol v. • Relative velocity The velocity of an object in relationship to another object

  6. Chapter 3Describing Motion • Average Acceleration

  7. Solution: The two bicycles will meet in one hour and if the bee travels at 30 km/hr. The bee will travel 30 km.

  8. Chapter 3 Describing Motion When the Smiths went on their vacation they traveled at 40 km/hr. They returned home at a rate of 60 km/hr. 40 km/hr > 60 km/hr QUESTION: What was their average rate of speed?

  9. Solution

  10. Chapter 3 Describing Motion but if ti = 0, then vf = vi + at Substitute for vf

  11. Chapter 3 Describing Motion Solve both equations for t vf = vi +at Set equal to each other Multiply across Simplify vf 2 = vi2 + 2ad (vf - vi)(vi + vf) = 2ad

  12. Chapter 3 Describing Motion vf = vi +at ag = -9.8 m/s2 ag = -32 ft/s2 vf 2 = vi2 + 2ad

  13. Ima Hurryin approaches a stoplight in her car which is moving with a velocity of +30.0 m/s. The light turns yellow, Ima applies the brakesand skids to a stop. If Ima's acceleration is –8.00 m/s2, determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a positive (+) and a negative (–) sign, respectively.) Chapter 3Describing Motion

  14. Chapter 3Describing Motion Given: vi = +30.0 m/s vf = 0 m/s a = –8.00 m/s2 Find: d = ?? Diagram:

  15. Chapter 3Describing Motion • (0 m/s)2 = (30.0 m/s)2 + 2*(-8.00 m/s2)*d • 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2)*d • (16.0 m/s2)*d = 900 m2/s2 - 0 m2/s2 • (16.0 m/s2)*d = 900 m2/s2 • d = (900 m2/s2)/ (16.0 m/s2) • d = 56.3 m

  16. Chapter 3Describing Motion Ben Rushin is waiting at a stoplight in his car, When the light turns green, Ben accelerates from rest at a rate of a 6.00 m/s2for an interval of 4.10 seconds. Determine the displacement of Ben's car during this time period. Given: Find: vi = 0 m/s d =? t = 4.10 s a = 6.00 m/s2

  17. Chapter 3Describing Motion • d = (0 m/s)*(4.1 s) + 0.5*(6.00 m/s2)*(4.10 s)2 • d = (0 m) + 0.5*(6.00 m/s2)*(16.81 s2) • d = 0 m + 50.43 m • d = 50.4 m

  18. Chapter 3Describing Motion Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. Given: Find: vi = 0.0 m/s t = ?? d = –8.52 m a = –9.8 m/s2

  19. Chapter 3Describing Motion • -8.52 m = (0 m/s)*(t) + 0.5*(-9.8 m/s2)*(t)2 • -8.52 m = (0 m) *(t) + (-4.9 m/s2)*(t)2 • -8.52 m = (-4.9 m/s2)*(t)2 • (-8.52 m)/(-4.9 m/s2) = t2 • 1.739 s2 = t2 • t = 1.32 s

  20. Chapter 3 Describing Motion Motion Applet

  21. Chapter 3Describing Motion Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Given: Find: vi = 26.2 m/s d = ?? vf = 0 m/s a = –9.8 m/s2

  22. Chapter 3Describing Motion • (0 m/s)2 = (26.2 m/s)2 + 2*(-9.8m/s2)*d • 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2)*d • (-19.6 m/s2)*d = 0 m2/s2 -686.44 m2/s2 • (-19.6 m/s2)*d = -686.44 m2/s2 • d = (-686.44 m2/s2)/ (-19.6 m/s2) • d = 35.0 m

  23. Chapter 3Describing Motion An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until it finally lifts off the ground. Determine the distance traveled before take-off. • Given: • a = 3.20 m/s2 • t = 32.8 s • vi = 0 m/s • Find: • d = ?? • d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2 • d = 1720 m

  24. Upton Chuck is riding the Giant Drop at Great America. If Upton free-falls for 2.6 seconds, what will be his final velocity and how far will he fall? Chapter 3Describing Motion • Find: • d = ?? • vf = ?? • d = vi*t + 0.5*a*t2 • d = (0 m/s)*(2.6 s)+ 0.5*(-9.8 m/s2)*(2.6 s)2 • d = 33 m • vf = vi + a*t • vf= 0 + (-9.8 m/s2)*(2.6 s) • vf = -25.5 m/s (the negative sign indicates direction) • Given: • a = –9.8 m/s2 • t = 2.6 s • vi = 0 m/s

  25. Chapter 3Describing Motion A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike. • vf2 = vi2 + 2*a*d • (7.10 m/s)2 = (0 m/s)2 + 2*(a)*(35.4 m) • 50.4 m2/s2 = (0 m/s)2 + (70.8 m)*a • (50.4 m2/s2)/(70.8 m) = a • a = 0.712 m/s2

  26. Chapter 3Describing Motion • A car is traveling at 65 km/hr. The brakes • are applied and the car stops in 3 seconds. • What is the car’s acceleration? • How far does it travel? vi = 65 km/hr t = 3 s vf = 0 vi = 65 km/hr = 18m/s

  27. Chapter 3Describing Motion • A car is traveling at 65 km/hr. The brakes • are applied and the car stops in 3 seconds. • What is the car’s acceleration? • How far does it travel? vi = 18 m/s t = 3 s vf = 0

  28. Chapter 3Describing Motion • A car is traveling at 65 km/hr. The brakes • are applied and the car stops in 3 seconds. • What is the car’s acceleration? • How far does it travel? =27 m

  29. Chapter 3Describing Motion • An airplane must reach a speed of 55 m/s • before take off. It can accelerate at 12 m/s2. • How long does the runway have to be? • How long will this take? vi = 0 a = 12 m/s2 vf = 55 m/s

  30. Chapter 3Describing Motion • An airplane much reach a speed of 55 m/s • before take off. It can accelerate at 12 m/s2. • How long does the runway have to be? • How long will this take? vi = 0 a = 12 m/s2 vf = 55 m/s

  31. Chapter 3Describing Motion Joe is driving a car at 20 m/s and notices a cow in front of him at a distance of 80 m away. He brakes at a rate of 3 m/s2. What happens to the cow? vi = 20 m/s a = -3 m/s2 vf = 0

  32. Chapter 3Describing Motion The cow survives!!!!

  33. Chapter 3Describing Motion ag = -9.8 m/s2 For all free falling bodies on earth, they accelerate downward at 9.8 m/s2.

  34. Chapter 3Describing Motion • A ball is thrown upward at 49 m/s. • How long is it in the air? • How high does it go? • How fast is it going when it lands?

  35. Chapter 3Describing Motion • How long is it in the air? vi = 49 m/s a = -9.8 m/s2 vf = 0 Total time in air is 10 sec

  36. Chapter 3Describing Motion • How high does it go? vi = 49 m/s a = -9.8 m/s2 t = 5 sec

  37. Chapter 3Describing Motion • How fast is it going when it lands? vi = 49 m/s a = -9.8 m/s2 t = 10 sec

  38. Chapter 3Describing Motion Free Fall

  39. Chapter 3Describing Motion A skier travels from A to B to C to D. What is her average velocity and speed?

  40. Chapter 3Describing Motion Josh travels from A to B to C to D. What is his average velocity and speed? =46.7 m/min =140 m/min

  41. Chapter 3 Describing Motion When a traffic light turns green, a waiting car starts off with a constant acceleration of 6 m/s2. At the instant the car begins to accelerate, a truck with constant velocity of 21 m/s passes in the next lane. a. How far will the car travel before it overtakes the truck? b. How fast will the car be traveling when it overtakes the truck? c. Construct a distance vs time graph for the car and the truck on the same graph.

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