Question

determine the average acceleration of a slalom skier if she is moving at a velocity of 9.75 m/s[S25E] and then changes her velocity of 8.64 m/s [W35S] in a matter of 0.179sec.

Answer 1

original south = 9.75 cos 25
final south = 8.64 sin 35

original east = 9.75 sin 25
final east = -8.64 cos 35

south a component = (final south -original south)/ .179

east a component = (final east component - original east component) / .179

resultant mag of a = sqrt (south a^2 + east a^2 )

angle T south of east
tan T = final a south / final a east

Answer 2

acceleration=(vfinal-Vinitial)/time

Now, notice the velocity is vectors. I would do it like this
vf=9.75cos25 S + 9.75sin25 E
Vi=8.64sin35 S + 8.64cos35 W

remember W is -E, so when you subtract..
Vf-Vi=(9.75cos25 -8.64sin35)S +(9.75sin25+8.64cos35) E

do that math, divide by time

If you wish, change it to polar form, the problem did not require it.