# Change in Velocity: Find Solution and Reasoning

• yowatup
In summary, the homework problem involves finding the change in velocity using two given vectors, Va and Vb. The two possible solutions are to either subtract the vectors directly or to reverse the direction of Va and add it to Vb. The correct solution is the second method, as it follows the principle of vector subtraction.
yowatup

## Homework Statement

I am required to find the change in velocity given these two vectors:

Va = 4.4 m/s [E31*S]
Vb = 7.8 m/s [E25*N]

## Homework Equations

delta V = Vb - Va
delta V = Vb + (-Va)

## The Attempt at a Solution

I am stuck between two solutions:

#1. Simply subtracting the vectors:

V = Vb - Va
V = (7.8, 25*) - (4.4, 31*)
V = [7.1, 3.3] - [3.8, 2.3]
V = [3.3, 1.0]
V = (3.5, 16.8*)

#2. Reversing the direction of Va, its directionality becomes [W31*N], effectively 149*.

V = Vb + (-Va)
V = (7.8, 25*) + (4.4, 149*)
V = [7.1, 3.3] + [-3.8, 2.3]
V = (6.5, 59*)

Which solution is correct and why? The first would solution would be the same if you distributed -1 across to both terms, but I'm pretty sure that operation is not permitted.

Doesn't taking the negative vector mean that the -31 is really 149 + 180 = 329

I don't think so, as can be seen here:
http://i543.photobucket.com/albums/gg464/yowatupguystill/vector-1.jpg

EDIT: I might have been correct on my first attempt, but I had assumed that this was correct: https://www.physicsforums.com/archive/index.php/t-275728.html

Last edited by a moderator:
What is shown in your drawing is 329° and you are reversing it to 149° .

Yes. Is that not correct, given that we are reversing the direction?

Secondly, I have just drawn out a vector diagram to scale of the vectors in question. It seems to support #2, though I'm not sure how certain to be - given that I haven't work graphically with vectors in a while.

I believe Method 2 is the right way - the sum of the vector and the negative of a vector to do a vector subtraction..

## 1. How is change in velocity calculated?

Change in velocity is calculated by subtracting the initial velocity from the final velocity. The formula is ∆v = vf - vi, where ∆v is the change in velocity, vf is the final velocity, and vi is the initial velocity.

## 2. What causes a change in velocity?

A change in velocity can be caused by various factors, such as acceleration, deceleration, or change in direction. It can also be influenced by external forces, such as friction and gravity.

## 3. How does mass affect change in velocity?

According to Newton's Second Law of Motion, the change in velocity of an object is directly proportional to the force applied and inversely proportional to its mass. This means that the greater the mass of an object, the smaller its change in velocity will be for a given force.

## 4. Can change in velocity be negative?

Yes, change in velocity can be negative. A negative change in velocity indicates a decrease in speed, while a positive change in velocity indicates an increase in speed.

## 5. How is change in velocity related to acceleration?

Acceleration is the rate of change of velocity. This means that the greater the change in velocity over a given time period, the greater the acceleration will be. In other words, acceleration is a measure of how quickly an object's velocity is changing.

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