4_07 - measured in seconds with t between 0 and 8 seconds...

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A.P. Calculus – Additional Homework for Motion You may use your calculator 1. A particle is moving along the x -axis with velocity, ( 29 sin 2 v t t = , 0 t v . At time 2 t π = it has position x = 3. Find the total distance, s traveled by this particle on the interval 0 t π . 2. A particle is moving along the x -axis so that at time t its acceleration is ( 29 cos a t t π π = . At time t = ½, the velocity, v of the particle is ½. a) Find the velocity of the particle at any time t . b) Find the minimum velocity of the particle. c) Find the equation for the position x ( t ) if x (0) = 0. d) What is the first time t > 0 that the particle returns to the origin? 3. A particle is moving with velocity: 2 ( ) 9 18 = - + v t t t with distance, s measured in meters, left or right of zero, and
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Unformatted text preview: measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t = 0 sec is 1 meter right of zero. Find each of the following. Give units in the answer . a) The initial acceleration b) The average velocity over the interval 0 to 8 seconds c) The instantaneous velocity at time 5 secs d) The time(s) when the particle is at rest e) The time interval(s) when the particle is moving left f) The time interval(s) when the particle is moving right g) The speed of the particle at time 4 secs h) The time interval(s) when the particle is (i) going faster (ii) slowing down i) Find the total distance the particle has traveled between 0 and 8 seconds...
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