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

[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.

Homework Statement

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

Homework Equations

average acceleration = deltaV/deltaT

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...

 

[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).

 

[mfu]

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).

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...

 

[diazona]

For part (b), try it both ways and see if they agree. Remember the formula:

average acceleration = deltaV/deltaT

and also remember that since this is a vector formula, it really stands for three equations in one:
$$\bar a_x = \frac{\Delta v_x}{\Delta t}$$

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

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

 

[rdl]

Hello and welcome to physics! Vectors, change in velocity, and average acceleration are all important concepts in physics and will be covered extensively in your course. In this problem, we are dealing with a two-dimensional motion, which means we need to consider both the magnitude and direction of the velocity and acceleration.

To solve part (a), we can use the vector addition method to find the total change in velocity. First, we need to find the X and Y components of each vector. For the first vector, John is traveling 15 km west, so the X component is -15 km and the Y component is 0 km. For the second vector, he is traveling 7.0 km south, so the X component is 0 km and the Y component is -7.0 km. For the third vector, he is traveling 33 km southeast, so the X component is 33cos(45°) km and the Y component is -33sin(45°) km. We can use the Pythagorean theorem to find the magnitude of each component and then use the inverse tangent function to find the direction.

Using the vector addition method, we can add all of the X components together and all of the Y components together to find the total change in velocity. This will give us the magnitude in km/h and the direction in degrees south of east. Remember to keep track of the signs of the components, as they represent the direction of the velocity.

For part (b), we can use the formula for average acceleration to find the magnitude and direction. We already have the change in velocity from part (a), so we just need to divide it by the total time taken for the trip. This will give us the magnitude in km/h^2 and the direction in degrees south of east.

I hope this helps! Remember to always pay attention to the units and directions when dealing with vectors and motion in physics. Good luck with your studies!