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Velocity and Acceleration: Put
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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
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 Velocity, Toilet, Major League Baseball

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