A baseball is traveling at [tex](+30 \, \text{m/s})[/tex] and is hit by a bat. It leaves the bat traveling at [tex](-40 \, \text{m/s})[/tex].

What is the change in velocity?

A. [tex]-10 \, \text{m/s}[/tex]
B. [tex]-30 \, \text{m/s}[/tex]
C. [tex]-40 \, \text{m/s}[/tex]
D. [tex]-70 \, \text{m/s}[/tex]



Answer :

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]