7 Position and velocity of a car

# 7 Position and velocity of a car - Next Velocity of a...

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• davidvictor
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Next: Velocity of a falling Up: Velocity and Acceleration: Put Previous: Velocity and Acceleration: Put Position and velocity of a car Example In driving in a straight line from New York to Boston, your position function given in miles from New York is described by the function: where t is the number of hours since the trip began. It takes you 8 hours to get to Boston. a) Find your velocity at time t = 1/2 hrs. b) Do you ever backtrack during the trip? Solution to a): First, we find your velocity function at any time by differentiating your position function. v ( t ) = f '( t ) = 5 t 2 - 50 t + 120. Then, to find your velocity after half an hour, we just plug 1/2 into the velocity function. Hey, it sounds high but a lot of states have upped their speed limits. Solution to b) (Do you backtrack?): Yes you do. It seems you left your favorite Mets baseball cap at the rest stop when you took it off to check your thinning hair in the mirror. Passing through Providence, you noticed the shiny spot on your head when you looked in the rear view mirror and realized you had forgotten it. Unfortunately, when you got back to the rest stop, you

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