When an object is speeding up to the right along a straight line, which of the following statements is true about the directions of its velocity $\mathbf{v}$ and acceleration $\mathbf{a}$ vectors?

• A. Both the velocity $\mathbf{v}$ and acceleration $\mathbf{a}$ vectors point to the right.
• B. Both the velocity $\mathbf{v}$ and acceleration $\mathbf{a}$ vectors point to the left.
• C. The velocity vector $\mathbf{v}$ points to the right, but the acceleration vector $\mathbf{a}$ points to the left.
• D. The velocity vector $\mathbf{v}$ points to the left, but the acceleration vector $\mathbf{a}$ points to the right.

Answer: (A)

Verified step by step guidance

1. Understand that velocity vector \( \mathbf{v} \) indicates the direction of the object's motion. Since the object is speeding up to the right, its velocity vector points to the right.
2. Recall that acceleration vector \( \mathbf{a} \) represents the rate of change of velocity. When an object speeds up, acceleration is in the same direction as velocity.
3. Recognize that if the acceleration were opposite to the velocity, the object would be slowing down, not speeding up.
4. Therefore, for an object speeding up to the right, both velocity \( \mathbf{v} \) and acceleration \( \mathbf{a} \) vectors point to the right.
5. Summarize that the correct statement is: both the velocity and acceleration vectors point to the right.