Change in velocity as vector subtraction

Steps:

• Represent initial velocity as vector $\vec{u}$ from origin to point U.
• Represent final velocity as vector $\vec{v}$ from origin to point V.
• Change in velocity $\Delta \vec{v} = \vec{v} - \vec{u}$ is the vector from U to V.
• Match this to the choice showing the arrow from U's head to V's head.

Why C is correct:

• C depicts $\vec{v} - \vec{u}$, the true vector difference per the definition of velocity change in kinematics.

Why the others are wrong:

• A: Shows $\vec{v}$ alone, ignoring subtraction.
• B: Shows $\vec{u}$ alone, not the difference.
• D: Shows $\vec{u} + \vec{v}$, an incorrect sum.

Final answer: C