Displacement from Velocity: A cyclist pedals along a straight road with velocity

Question

Displacement from Velocity: A cyclist pedals along a straight road with velocity v(t)=(2t^2)-(8t)+(6) mi/hr for 0<=t<=3 , where t is measured in hours. a) Determine the intervals in which the cyclist moves in the positive direction and when she moves in the negative direction. b) Find the displacement of the cyclist (in miles) on the time interval [0,3]. c) Find the distance traveled over the interval [0,3].

Explanation / Answer

A)v(t) > 0. So solve for this. B)integrate v ato find x in limits 0 to 3. c) integrate |v| from oto3

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