SOLUTION: An object is moving in a straight line with velocity v(t)=3t^2 for t>0 . the dist traveled by the object during the time interval [2 3] is........
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Question 1083176: An object is moving in a straight line with velocity v(t)=3t^2 for t>0 . the dist traveled by the object during the time interval [2 3] is........
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Position is the antiderivative of velocity, so:
\ =\ \int\,v(t)\,dt\ =\ 3\int\,t^2\,dt\ =\ 3\,\cdot\,\frac{1}{3}t^3\ +\ C\ =\ t^3\ +\ C)
where the constant represents the initial position.
\ =\ 8\ +\ C)
\ =\ 27\ +\ C)
Distance over the interval is \ -\ p(2))
\ -\ (8\ +\ C)\ =\ 19\ \text{units})
John
My calculator said it, I believe it, that settles it
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