Kinematics question concerning the direction of avg acceleration

[justrandom94]

alright so here's a pretty straight forward question asking to find the avg acceleration:

A car with a velocity of 25m/s [E] changes its velocity to 25 m/s in 15s. Calculate
avg acceleration.

So i drew out the vector diagram, found the resultant velocity and solved for the avg acceleration. My answer was right but the direction was wrong. My answer was 2.4 m/s^2 [45 degrees south of east ]
however, the books answer is 2.4 m/s^2 [45 degrees S of W] Can anyone explain to me
why it is south of WEST and not East?

 

[genericusrnme]

if the acceleration was all going south and east then the velocity would only increase in the south and east directions
after the cars velocity has changed, what happened to the eastward component of velocity?

 

[justrandom94]

when i drew it out first i drew out the east ward vector then the south one, and the resultant vector connecting the two allows me to use Pythagorean therom so no components were needed to find the resultant velocity, the east velocity and south velocity are at right angles to one another

 

[SammyS]

alright so here's a pretty straight forward question asking to find the avg acceleration:

A car with a velocity of 25m/s [E] changes its velocity to 25 m/s in 15s. Calculate
avg acceleration.

So i drew out the vector diagram, found the resultant velocity and solved for the avg acceleration. My answer was right but the direction was wrong. My answer was 2.4 m/s^2 [45 degrees south of east ]
however, the book's answer is 2.4 m/s^2 [45 degrees S of W] Can anyone explain to me
why it is south of WEST and not East?

You need to find the change in velocity, divided by the elapsed time.

\vec{\Delta v}=\vec{v}_{\text{final}}-\vec{v}_{\text{initial}}

You can also find the change in velocity by asking yourself: what vector must be added to the initial velocity so that the resultant is equal to the final velocity?

\vec{v}_{\text{final}}=\vec{v}_{\text{initial}}+ \vec{\Delta v}​

 

[genericusrnme]

when i drew it out first i drew out the east ward vector then the south one, and the resultant vector connecting the two allows me to use Pythagorean therom so no components were needed to find the resultant velocity, the east velocity and south velocity are at right angles to one another

okay, the vector that points from the initial velocity to the final velcity, it is the one that gives you the change in velocity, what way is that vector facing?