A motorboat starting from a dead stop accelerates at an average rate of 2.0 m/s^2 for 3 seconds, then very rapidly roars up to 4.0m/s^2 for 4 seconds. Finally, it decelerates to a stop 20 seconds later at a rate of 1.1m/s^2.
(a) What is its average acceleration during the first 27 seconds?
(b) What is its instantaneous acceleration 10 seconds into the trip?
average acceleration = (v(f)-v(i)) / (f - i)
v = v(0) + at
The Attempt at a Solution
From t=0.0s to 3.0s,
v(0) = 0m/s
v(3) = 0 + 2.0 * 3 = 6.0m/s
From t=3.0s to 7.0s,
v(0) = v(3) ==> due to re-setting the frame of reference so t=3.0s => t=0.0s
v(4) = v(7) = 6.0 + 4.0*4 = 22m/s
From t=7.0s to 27.0s
v(final) = v(27) = 0.0m/s since it comes to a stop
average acceleration from t=7.0s to t=27.0s = -1.1m/s^2
Applying the average acceleration formula, -1.1 = (0 - V(i)) / 20, V(i) = v(7) = 22m/s
By following the average acceleration formula, I would all too easily get zero as average since V(i) and V(f) are both zero. What am I not seeing here?