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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 back-and-forth trip until the bikes meet, and squish! How many kilometers did the bee travel in its total back-and 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