3. Example : If a car traveling at 28 m/s is brought to a full stop 4.0 s after the brakes are applied, find the average acceleration during braking. Given: vi = +28 m/s, vf= 0 m/s, and t = 4.0 s.
4. The time can be found from the average acceleration, At highway speeds, a particular automobile is capable of an acceleration of about 1.6 m/s2. At this rate, how long does it take to accelerate from 80 km/h to 110 km/h? .
6. The average velocity of an object during a time interval t is The acceleration, assumed constant, is 2-5 Motion at Constant Acceleration
7. In addition, as the velocity is increasing at a constant rate, we know that Combining these last three equations, we find:
8. We can also combine these equations so as to eliminate t: Motion with Constant Acceleration We now have all the equations we need to solve constant-acceleration problems.
15. The sprinter starts from rest. The average acceleration is found from the elapsed time is found by solving A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter, and how long does it take her to reach that speed?
16. The words “slowing down uniformly” implies that the car has a constant acceleration. The distance of travel is found form A car slows down uniformly from a speed of 21.0 m/s to rest in 6.00 s. How far did it travel in that time? .
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18. 2-5. Free Fall The acceleration of gravity (g) for objects in free fall at the earth's surface is 9.8 m/s2. Galileo found that all things fall at the same rate.
19. 2-5. Free Fall The rate of falling increases by 9.8 m/s or 10 every second. Height = ½ gt2 For example: ½ (9.8 )12 = 4.9 m½(9.8)22 = 19.6 m ½ (9.8)32 = 44.1 m ½ (9.8)42 = 78.4 m
20. 2-5. Free Fall A ball thrown horizontally will fall at the same rate as a ball dropped directly.
21. 2-5. Free Fall A ball thrown into the air will slow down, stop, and then begin to fall with the acceleration due to gravity. When it passes the thrower, it will be traveling at the same rate at which it was thrown.
30. Foucault Pendulum Inertia keeps a pendulum swinging in the same direction regardless of the motion of the earth. This can be used to measure the motion of the earth. As the Foucault Pendulum swings it appears to be rotating, but it is the earth that is rotating under it. To the right is the Foucault Pendulum at the Pantheon in Paris, France.
31. Foucault Pendulum Other Web sites that illustrate the Foucault Pendulum. http://en.wikipedia.org/wiki/File:Foucault-rotz.gif http://www.physclips.unsw.edu.au/jw/foucault_pendulum.html http://aspire.cosmic-ray.org/labs/scientific_method/pendulum.swf http://www.calacademy.org/products/pendulum/page7.htm http://www.youtube.com/watch?v=nB2SXLYwKkM
32. 2-8. Mass Inertia is the apparent resistance an object offers to any change in its state of rest or motion.
33. 2-9. Second Law of Motion Newton's second law of motion states: The net force on an object equals the product of the mass and the acceleration of the object. The direction of the force is the same as that of the acceleration. F = Ma
34. 2-9. Second Law of Motion A force is any influence that can cause an object to be accelerated. The pound (lb) is the unit of force in the British system of measurement: 1 lb = 4.45 N (1 N = 0.225 lb)
38. 2-12. Circular Motion Centripetal force is the inward force exerted on an object to keep it moving in a curved path. Centrifugal force is the outward force exerted on the object that makes it want to fly off into space.
44. This illustrates the way scientists can use indirect methods to perform seemingly “impossible tasks”= mg
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46. 2-15. Artificial Satellites The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h.
47. 2-15. Artificial Satellites The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h.