# Resultant vector given initial velocity and acceleration

• idllotsaroms
In summary, the conversation is about finding the correct vector representation of an upward acceleration acting on a body with an initial velocity and in a positive x-direction. The student initially attempted to add the acceleration and velocity vectors together, but was reminded that they have different units and that a qualitative answer is needed. They then eliminated some options and concluded that the correct answers are B and D.
idllotsaroms

## Homework Statement

http://postimage.org/image/466vu4yvp/
http://postimage.org/image/opdrmlv5n/

There can be more than one right answer

α=Δv/ΔX
v = v0 + αt

## The Attempt at a Solution

Im having difficulty understanding the upward acceleration vector. Because I set the +y direction as positive (up) and the +x-direction as positive (right). So I thought that if acceleration is up, it means that acceleration is positive so the velocity is increasing (just a vector that is the exact same as the Vo vector).
I attempted to add the two vectors together (hypotenuse) and say that was the answer, but it was incorrect (45° angle vector).

Last edited:
You can't add an acceleration vector to a velocity vector; they have different units. And since you don't have any magnitudes and don't know how long the force acted, you are looking for a qualitative answer, not a quantitative one (that is, you couldn't have gotten a 45 degree angle). You are on the right track, though. Look at the possible answers and see if you can eliminate any of them.

I guess my question then is, how am I supposed to add two unlike vectors?
So far, I eliminated A because I believe it doesn't make sense for there not to be a velocity vector.
C seems unlikely because of the initial velocity
E seems unlikely because that straight vector pointed right doesn't have the acceleration acting on it.
Would the answer be B and D, because they are the only resulting vectors that have the depicted upward acceleration acting on them with still pointing to the positive X-direction?

idllotsaroms said:
I guess my question then is, how am I supposed to add two unlike vectors?
You don't need exact results, just a general idea of what the effects of the force would be.
So far, I eliminated A because I believe it doesn't make sense for there not to be a velocity vector.
Right.
C seems unlikely because of the initial velocity
Right.
E seems unlikely because that straight vector pointed right doesn't have the acceleration acting on it.
Right.
Would the answer be B and D, because they are the only resulting vectors that have the depicted upward acceleration acting on them with still pointing to the positive X-direction?
Right.

... I swear I attempted that solution D:, but I tried it again and it worked! I think I accidentally submitted my response incorrectly!

Thank you tms for your help! (I was on my last attempt)

## 1. What is a resultant vector?

A resultant vector is a single vector that represents the combined effect of two or more individual vectors. It is the sum of all the individual vectors' magnitudes and directions.

## 2. How is initial velocity related to the resultant vector?

Initial velocity is one of the components that determines the magnitude and direction of the resultant vector. It is the starting velocity of an object and is represented as a vector with a specific magnitude and direction.

## 3. What is the role of acceleration in calculating the resultant vector?

Acceleration is another component that affects the magnitude and direction of the resultant vector. It describes the rate of change of an object's velocity over time and is also represented as a vector with a specific magnitude and direction.

## 4. How do you calculate the resultant vector given initial velocity and acceleration?

The resultant vector can be calculated using the Pythagorean theorem, which states that the magnitude of the resultant vector is equal to the square root of the sum of the squares of the individual vectors' magnitudes. The direction of the resultant vector can be calculated using trigonometric functions such as sine, cosine, and tangent.

## 5. Can the resultant vector be negative?

Yes, the resultant vector can be negative. This means that the direction of the resultant vector is in the opposite direction of the initial velocity vector. It is important to consider both the magnitude and direction of the resultant vector to fully understand the motion of an object.

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