Finding average accleration..?

Question

An Iceboat sails across the surface of a frozen lake with constant acceleration produced by the wind. At a certain instant, the boat's velocity is V_1 = (6.30 m/s)i^ +(-8.42 m/s)j^. Three seconds later, because of a wind shift, the boat is instantaneously at rest. What is it's average acceleration for this 3 second interval? Explain.

i^ = i hat, j^ = j hat

Answer 1

The average acceleration in the time interval (t, t+x) is given by the following formula:

a = (v(t+x) - v(t)) / x.

This means the change of speed per time unit, which is a rather intuitive concept for average acceleration. Similarly, the average velocity in the time interval (t, t+x) is given by:

v = (s(t+x) - s(t)) / x, i.e., the change of the distance travelled per time unit.

Thus, in our case, we have the following data:

x = 3 (length of time interval)
v(t+3) = 0i^ + 0j^, i.e., the velocity after 3 seconds is 0, because the text says that the boat is at rest after three seconds.
v(t) is the same as what you gave as V_1

We get the average acceleration by substituting these data into the formula:

a = ((6.3 m/s)i^ + (-8.42 m/s)j^ - (0i^ + 0j^)) / 3 = (2.1 m/s)i^ + (-2.8066)j^.

Answer 2

The initial vector velocity magnitude is sqrt(6.30^2+8.42^2). Three seconds later it is zero. The average acceleration is the initial velocity divided by 3