Question

A car is traveling due east. Its velocity (in miles per hour) at time t hours is given by v(t) = -2.5t^2 + 10t + 50. How far did the car travel during the first seven hours of the trip? miles.

          A car is traveling due east. Its velocity (in miles per hour) at time t hours is given by
v(t) = -2.5t^2 + 10t + 50.
How far did the car travel during the first seven hours of the trip?
miles.
        
A car is traveling due east. Its velocity (in miles per hour) at time t hours is given by
v(t) = -2.5t^2 + 10t + 50.
How far did the car travel during the first seven hours of the trip?
miles.

Added by Richard G.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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A car is traveling due east. Its velocity (in miles per hour) at time t hours is given by v(t) = -2.5t^2 + 10t + 50. How far did the car travel during the first seven hours of the trip? miles.
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Transcript

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00:01 Hi, in this question we are given with the velocity as a function of t and this is equals to minus 2 .5 times t squared plus 10 times t plus 50 with which a car is traveling and we need to find the distance travel by the car from first seven hours of the trip.
00:24 That means we need to find the distance as we know the distance s will be equals to integration of the velocity.
00:30 Times d t from 0 to 7 and this will be equals to integration from 0 to 7 minus 2 .5 times t squared plus 10 times t plus 50 times t and solving this further we get this to be equals to minus 2 .5 times t raised 2 par 3 by 3 plus 10 times t squared by 2 plus 50 times and the limits from 0 to 7.
01:05 Now substituting the limits we get minus 2 .5 by 3 times 7 raised to par 3 plus 5 times 7 plus 50 times 7...
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