The average acceleration vector must point in the same direction as which of the following vectors?

• A. The displacement vector, $∆x$
• B. The initial velocity vector, $v_0$
• C. The change in velocity vector, $∆v$
• D. The position vector, $r$

Answer: (C)

Verified step by step guidance

1. Recall the definition of average acceleration: it is the change in velocity divided by the time interval over which the change occurs. Mathematically, average acceleration \( \vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t} \).
2. Understand that \( \Delta \vec{v} \) is the vector difference between the final velocity \( \vec{v} \) and the initial velocity \( \vec{v}_0 \), so \( \Delta \vec{v} = \vec{v} - \vec{v}_0 \).
3. Since average acceleration is directly proportional to \( \Delta \vec{v} \) and the time interval \( \Delta t \) is a scalar, the direction of average acceleration must be the same as the direction of the change in velocity vector \( \Delta \vec{v} \).
4. Note that the displacement vector \( \Delta \vec{x} \) and the position vector \( \vec{r} \) describe spatial changes and locations, but they do not determine the direction of acceleration.
5. Therefore, the average acceleration vector points in the same direction as the change in velocity vector \( \Delta \vec{v} \), not the displacement, initial velocity, or position vectors.