Certainly! When considering the change in velocity, it's crucial to take into account both the magnitude and the direction of the velocities involved, as velocity is a vector quantity.
Here's how you can solve it step by step:
1. Identify the initial velocity: The initial velocity of the baseball is \( +30 \, \text{m/s} \). The positive sign indicates that the baseball is moving in a specific direction which we will call the positive direction.
2. Identify the final velocity: The final velocity of the baseball is \( -40 \, \text{m/s} \). The negative sign indicates that the baseball is moving in the opposite direction (negative direction).
3. Calculate the change in velocity: The change in velocity (\(\Delta v\)) is given by the formula:
[tex]\[
\Delta v = \text{Final Velocity} - \text{Initial Velocity}
\][/tex]
Substituting the known values:
[tex]\[
\Delta v = -40 \, \text{m/s} - (+30 \, \text{m/s})
\][/tex]
4. Simplify the expression:
[tex]\[
\Delta v = -40 \, \text{m/s} - 30 \, \text{m/s}
\][/tex]
5. Perform the subtraction:
[tex]\[
\Delta v = -40 - 30 = -70 \, \text{m/s}
\][/tex]
Hence, the change in velocity of the baseball is \(-70 \, \text{m/s}\).
Therefore, the correct answer is:
- [tex]\(-70 \, \text{m/s}\)[/tex]
