At time t or= to 0, the position of a particle moving along the x-axis is given by x(t)= (t^3/3)+2t+2. For what value of t in the interval [0,3] will the instantaneous velocity of the particle equal the average velocity of the particle from time t=0 to time t=3?

Question

At time t >or= to 0, the position of a particle moving along the x-axis is given by x(t)= (t^3/3)+2t+2. For what value of t in the interval [0,3] will the instantaneous velocity of the particle equal the average velocity of the particle from time t=0 to time t=3?

Steve · Accepted Answer

The average velocity for t in [0,3] is the distance traveled divided by the time spent: av = [x(3)-x(0)]/(3-0) = 17/3 So, we want t where x' = t^2 + 2 = 17/3 t^2 = 11/3, so t=1.9 seconds

Erin · Answer

That is wrong^ av=11-2/3= 9/3=3