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Chapter 3.1 Notes

Chapter 3.1 Notes . Rate. The speed of an object is the ratio of distance in a given time. You can measure speed with a stop watch and a meter stick. Speed = Distance / time S = d/t This equation tells us the speed if the speed is constant.

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Chapter 3.1 Notes

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  1. Chapter 3.1 Notes Rate

  2. The speed of an object is the ratio of distance in a given time. • You can measure speed with a stop watch and a meter stick. • Speed = Distance / time • S = d/t • This equation tells us the speed if the speed is constant

  3. If the speed varies, than we must find the average speed. • Average speed = change in distance / change in time • Vave = rd / rt

  4. You leave home and drive 100 miles east. The trip takes 2 hours. On the return trip you drive through a rainstorm and take 3 hours driving the same 100 miles. • Calculate the average speed driving to your friend’s house. • Calculate the average speed driving from your friend’s house. • Calculate the average speed for the entire trip

  5. You leave home and drive 100 miles east. The trip takes 2 hours. On the return trip you drive through a rainstorm and take 3 hours driving the same 100 miles. • Calculate the average speed driving to your friend’s house. • Vave = rd / rt • Vave = 100 miles / 2 hrs • Vave = 50 miles/hr

  6. You leave home and drive 100 miles east. The trip takes 2 hours. On the return trip you drive through a rainstorm and take 3 hours driving the same 100 miles. • Calculate the average speed driving from your friend’s house. • Vave = rd / rt • Vave = 100 miles / 3 hrs • Vave = 33.3 miles/hr

  7. You leave home and drive 100 miles east. The trip takes 2 hours. On the return trip you drive through a rainstorm and take 3 hours driving the same 100 miles. • Calculate the average speed for the entire trip • Vave = rd / rt • Vave = 200 miles / 5 hrs • Vave = 40 miles/hr

  8. The speed at any one instant is called the instantaneous speed. • The instantaneous speed can be found in a car with the speedometer.

  9. When we state the speed and direction of an object, we are stating the object’s Velocity. • Velocity tells us direction and size so it is a vector. • Speed tells us only size so it is a scalar.

  10. If you have a car going at a constant speed and driving on a circular path, is the velocity constant? • Velocity depends on both speed and direction. • The speed is constant. • Is the direction constant (North only)? • No – so the Velocity is not constant.

  11. The vector that defines the distance and direction between two positions is called displacement. • Displacement is like a short cut directly from one point to another.

  12. Average velocity =displacement/time • V = d/t

  13. If you have a displacement of 145 km and your flight takes 2 hours, what is your average velocity? • v = d/t • v = 145 km / 2 hrs • v = 72.5 km/hr

  14. The rate of change of an object’s velocity is the acceleration. (How fast you speed up or how fast you slow down) • Acceleration is a vector.

  15. Average acceleration = change in velocity / time • A = (Vf – Vi) / t

  16. A pilot increases the takeoff speed of an airplane from 20 ft/s to 200 ft/s in 30 seconds. What is the average acceleration? • A = (Vf – Vi) / t • A = (200 ft/s – 20 ft/s) / 30 s • A = 180 ft/s / 30 s • A = 6 ft/s2

  17. Speed and velocity are rates of linear motion. (in a straight line) • Angular speed is a rate of rotational motion.

  18. Angular speed = angular displacement/ time • w = rθ/rt • Angle = # of turns x 2pi

  19. If we have a tire that rotates 30 times in 60 seconds, what is the angular speed of the tire? • w = rθ/rt • Θ=# of turns x 2 pi • Θ = 30 x 2 pi • Θ = 188.4 rad • w = 188.4 rad / 60 s • w = 3.14 rad /s

  20. Speed = radius x angular speed • v = r x w

  21. A vacuum cleaner has a shaft that is 1.5 inches in diameter and turns at an angular speed of 2000 rad/s, what is the speed of the belt connected to this shaft? • v = r x w • radius = diameter/2 • r = 1.5 / 2 = .75 • v = .75 in x 2000 rad/s • v = 1500 in/s

  22. Change in angular speed = angular acceleration • The angular acceleration is the ratio of the change in angular speed to the time interval.

  23. Angular acceleration = change in angular speed / time • α = (wf – wi)/t

  24. A car’s brake is applied to a wheel for 5 seconds, reducing the wheel’s angular speed from 220 rad/sec to 180 rad/sec. What is the angular acceleration? • α = (wf – wi)/t • α = (180 rad/s – 220 rad/s)/5 s • α = -40 rad/s / 5 s • α = -8 rad/s2

  25. Position Time Graph

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