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Unformatted text preview: Chapter 2 : Motion along a Straight Line 1. Displacement and Average Velocity
Position : the location of an object Displacement : the direction and distance of the shortest path between an initial and final position: x f  xi Velocity : speed and direction, unit : m/s r A r B r r A B
r r r r = r2  r1 Average velocity : displacement divided by elapsed time. vave x2  x1 x = = t2  t1 t Opposite direction of motion Graphical analysis average speed = slope between two points Conceptual question) Suppose you wish to average 40 km/h on a particular trip and find that when you are half way to your destination you have only averaged 20 km/h. How fast would you have to travel on the remaining half of your trip to attain the overall average of 40 m/h? a) 60 km/h b) 80 km/h c) 90 km/h d) 120 km/h Example) Suppose in making a round trip you travel at a uniform speed of 30 km/h from A to B, and return from B to A at a uniform rate of 60 km/h. What would be your average speed for the round trip? a) 40 km/h b) 45 km/h c) 50 km/h When the 10 km/hr bikes are 20 km apart, a bee begins flying from one wheel to the other at a steady speed of 30 km/hr. When it gets to the wheel it abruptly turns around and flies back to touch the first wheel, then turns around and keeps repeating the backandforth trip until the bikes meet, and squish! How many kilometers did the bee travel in its total backand forth trips? 2. Instantaneous Velocity x dx vx = lim = t 0 t dt 3. Average and Instantaneous Acceleration
Acceleration : change in velocity, unit m/s2 Average acceleration aave v2  v1 v = = t2  t1 t Instantaneous acceleration v dv d 2 x a = lim = = 2 t 0 t dt dt 4. Motion with Constant Acceleration
Motion with constant positive acceleration results in steadily increasing velocity. Equations for constant acceleration motion vx (t ) = v0 x + ax t 1 2 x(t ) = x0 + v0 x t + ax t 2
2 2 vx = v0 x + 2ax ( x  x0 ) v0 x + vx x  x0 = 2 t Example 2.4) A motorist heading east through a small city
accelerates after he passes the signpost marking the city limits. His acceleration is a constant 4.0 m/s2. At t=0, he is 5.0 m east of the signpost, moving east at 15m/s a) Find his position and velocity at t=2.0 s. b) Where is he when his velocity is 25 m/s? Example 2.5) A motorist traveling with constant velocity of 16 m/s
passes a school cross corner, where the speed limit is 11.2 m/s. Just as he passes, a police officer on a motorcycle stopped at the corner starts off in pursuit in 2 s later with a constant acceleration of 3.0 m/s2. a) How long will it take to catch up? b) What is the officer's speed at that point? c) What is the total distance a police officer has traveled at that point? Problem 2.21) An antelope moving with constant acceleration
covers two points 70.0 m apart in 7.00 s. Its speed at the 2nd point is 15.0 m/s. a) What is its speed at 1st point? b) What is the acceleration? Example 2.7) You throw a ball vertically upward from the roof of a
tall building. The ball leave your hand at a point even with roof railing with a upward speed of 15.0 m/s; the ball is then in free fall. On its way back down, it just misses the railing. Find a) the position and velocity of the ball 1.00 s and 4.00 s after leaving your hand b) the velocity when the ball is 5.00 m above the railing c) the maximum height reached and time at maximum d) acceleration of the ball at maximum. 5. Free Falling Bodies
constant acceleration of free fall: 9.8 m/s2 due to the gravity This number is true near the earth's surface. Penny and feather Galileo's experiment on the moon. ...
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 Fall '08
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