# Vectors (?), Change in Velocity, Average Accel.

1. Jun 6, 2010

### mfu

Nice to meet you all. While this may be my first post here, I will be here quite often for the next year because I'll be taking physics.

1. The problem statement, all variables and given/known data
John drives 15 km directly west from Orion to Chester at a speed of 86 km/h, then directly south for 7.0 km to Seiling at a speed of 85 km/h, then finally 33 km southeast to Oakwood at a speed of 91 km/h. Assume he travels at constant velocity during each of the three segments.

(a) What was the change in velocity during this trip? [Hint: Do not assume he starts from rest and stops at the end.]
>magnitude in km/h
>direction in ° south of east

(b) What was the average acceleration during this trip?
>magnitude in km/h2
>direction in ° south of east

2. Relevant equations
average acceleration = deltaV/deltaT

3. The attempt at a solution
(a) I've tried finding the X & Y components of each section, and using the distance formula to determine the displacement(?), and dividing that by the time taken on the trip (which I found by dividing the length of each vector by the speed and mashing it together), but it turned out to be incorrect...
So then I tried to average the deltaV's of the first two & last two velocities, whcih wasn;t right either...
All of the book examples & teacher's example only had two different velocities, while this one has three, so I am at a total loss as to what I should do...

2. Jun 6, 2010

### diazona

Cnange in velocity is equal to final velocity minus initial velocity. That's a definition: change in ___ = final ___ minus initial ___. You'll be seeing (or at least using) that a lot, so make sure you remember it.

See if you can use that to answer part (a).

3. Jun 6, 2010

### mfu

OH WOW. It worked. Just needed to ignore the middle velocity they gave. Thank you very much!

For part (b), the direction of the acceleration should be the same as the direction of the velocity, right? Or should I find the X&Y components of the acceleration and take the arctan of that? Wanna verify first since I've already submitted answers 6 times, and the teacher never told us the submission limit...

4. Jun 6, 2010

### diazona

For part (b), try it both ways and see if they agree. Remember the formula:
and also remember that since this is a vector formula, it really stands for three equations in one:
$$\bar a_x = \frac{\Delta v_x}{\Delta t}$$

$$\bar a_y = \frac{\Delta v_y}{\Delta t}$$

$$\bar a_z = \frac{\Delta v_z}{\Delta t}$$