Dr. James is leaving London for a much needed winter vacation! Unfortunately, his car has been broken for several months, so his speedometer (which measures velocity) and clock (which measures time) both work, but his odometer (which measures distance travelled) does not. He starts his drive out of the city, but finds himself stuck in traffic. Being bored, and also being a mathematician, he starts to notice that his car’s velocity is a function of the time in hours he has spent on the road. Specifically, after t hours, his velocity (according to his speedometer) is v(t) = 8t**2 If it takes him 3 hours to get onto the highway out of London, determine the total distance he has travelled in those 3 hours. [HINT: You may wish to recall that velocity is the derivative of distance as a function of time. Reverse this relationship to get yourself started!]
the question below does not provide sufficient info, i could not apply the vt dt antiderivative formula. I do not know what to do.
Dr. James is leaving London for a much needed winter vacation!
Unfortunately, his car has been broken for several months, so his speedometer
(which measures velocity) and clock (which measures time) both work, but his
odometer (which measures distance travelled) does not.
He starts his drive out of the city, but finds himself stuck in traffic. Being bored,
and also being a mathematician, he starts to notice that his car’s velocity is
a function of the time in hours he has spent on the road. Specifically, after t
hours, his velocity (according to his speedometer) is
v(t) = 8t**2
If it takes him 3 hours to get onto the highway out of London, determine the
total distance he has travelled in those 3 hours.
[HINT: You may wish to recall that velocity is the derivative of distance as a
function of time. Reverse this relationship to get yourself started!]
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