1. Chapter 3.1 Notes Rate

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

4. If the speed varies, than we must find the average speed. If the speed varies, than we must find the average speed. Average speed = change in distance / change in time Average speed = change in distance / change in time V ave =  d /  t V ave =  d /  t

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. 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 to your friend’s house. Calculate the average speed driving from your friend’s house. Calculate the average speed driving from your friend’s house. Calculate the average speed for the entire trip Calculate the average speed for the entire trip

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. 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 to your friend’s house. V ave =  d /  t V ave =  d /  t V ave = 100 miles / 2 hrs V ave = 100 miles / 2 hrs V ave = 50 miles/hr V ave = 50 miles/hr

8. 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. 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. Calculate the average speed driving from your friend’s house. V ave =  d /  t V ave =  d /  t V ave = 100 miles / 3 hrs V ave = 100 miles / 3 hrs V ave = 33.3 miles/hr V ave = 33.3 miles/hr

9. 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. 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 Calculate the average speed for the entire trip V ave =  d /  t V ave =  d /  t V ave = 200 miles / 5 hrs V ave = 200 miles / 5 hrs V ave = 40 miles/hr V ave = 40 miles/hr

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

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

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

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

14. Average velocity =displacement /time Average velocity =displacement /time Average velocity Average velocity V = d/t V = d/t

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

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

17. Average acceleration = change in velocity / time Average acceleration = change in velocity / time Average acceleration Average acceleration A = (V f – V i ) / t A = (V f – V i ) / t

19. 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 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 = (V f – V i ) / t A = (V f – V i ) / t A = (200 ft/s – 20 ft/s) / 30 s A = (200 ft/s – 20 ft/s) / 30 s A = 180 ft/s / 30 s A = 180 ft/s / 30 s A = 6 ft/s 2 A = 6 ft/s 2

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

21. Angular speed = angular displacement/ time Angular speed = angular displacement/ time Angular speed angular displacement Angular speed angular displacement w =  θ/  t w =  θ/  t w =  θ/  t w =  θ/  t Angle = # of turns x 2pi Angle = # of turns x 2pi

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

23. Speed = radius x angular speed Speed = radius x angular speed v = r x w v = r x w

24. 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? 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 v = r x w radius = diameter/2 radius = diameter/2 r = 1.5 / 2 =.75 r = 1.5 / 2 =.75 v =.75 in x 2000 rad/s v =.75 in x 2000 rad/s v = 1500 in/s v = 1500 in/s

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

26. Angular acceleration = change in angular speed / time Angular acceleration = change in angular speed / time α = (w f – w i )/t α = (w f – w i )/t

27. 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? 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 = (w f – w i )/t α = (w f – w i )/t α = (180 rad/s – 220 rad/s)/5 s α = (180 rad/s – 220 rad/s)/5 s α = -40 rad/s / 5 s α = -40 rad/s / 5 s α = -8 rad/s 2 α = -8 rad/s 2

28. Position Time Graph Position Time Graph