Question

chapter 4 review

1. initial velocity vector $vec{v}_{0}$ and final velocity vector $vec{v}$ are shown below.

which of the following represents the change in velocity $deltavec{v}$?
a
b
c
d

Explanation:

Step1: Recall velocity - change formula

The change in velocity $\Delta\vec{V}=\vec{V}-\vec{V}_{0}$, which is equivalent to $\Delta\vec{V}=\vec{V}+(-\vec{V}_{0})$. To find $\Delta\vec{V}$, we can use the vector - addition rules. If we place the tail of $\vec{V}$ at the head of $-\vec{V}_{0}$ (where $-\vec{V}_{0}$ has the same magnitude as $\vec{V}_{0}$ but opposite direction), the vector from the tail of $-\vec{V}_{0}$ to the head of $\vec{V}$ represents $\Delta\vec{V}$.

Step2: Analyze vector directions

We know that $\vec{V}_{0}$ is a horizontal vector pointing to the right and $\vec{V}$ is a vector pointing in a different direction. When we subtract $\vec{V}_{0}$ from $\vec{V}$, we can think of it as adding $\vec{V}$ and the negative of $\vec{V}_{0}$. Geometrically, if we reverse the direction of $\vec{V}_{0}$ and then use the head - to - tail method of vector addition with $\vec{V}$, we find that the correct vector for $\Delta\vec{V}$ is the one that starts from the tail of the reversed $\vec{V}_{0}$ and ends at the head of $\vec{V}$.

Answer:

A.