Understanding Baseball Acceleration During Impact

Let's break down this physics problem about baseball acceleration during impact. We are given the initial velocity of a baseball, its final velocity after being hit by a bat, and the duration of the impact. Our goal is to find the acceleration of the baseball during this short time.

Defining Initial and Final Velocities

First, we need to be careful about the direction of velocity. Velocity is a vector quantity, meaning it has both magnitude and direction. Let's assume the initial direction of the baseball is positive.

• Initial velocity ($\vec{v}_{initial}$): $+25$ m/s (towards the bat)
• Final velocity ($\vec{v}_{final}$): $-35$ m/s (in the opposite direction, away from the bat)

The time duration of the impact is given as $\Delta t = 0.010$ s. This short impact time leads to a significant velocity change.

Calculating the Change in Velocity

The change in velocity ($\Delta \vec{v}$) is the difference between the final velocity and the initial velocity:

$$\Delta \vec{v} = \vec{v}_{final} - \vec{v}_{initial}$$

Plugging in the values:

$$\Delta \vec{v} = (-35 \text{ m/s}) - (25 \text{ m/s})$$

$$\Delta \vec{v} = -35 \text{ m/s} - 25 \text{ m/s}$$

$$\Delta \vec{v} = -60 \text{ m/s}$$

The negative sign indicates that the overall change in velocity is in the direction opposite to the initial motion. This large velocity change occurs over a very short impact time.

Determining the Baseball's Acceleration

Acceleration ($\vec{a}$) is defined as the rate of change of velocity. It is calculated by dividing the change in velocity by the time interval over which the change occurs:

$$\vec{a} = \frac{\Delta \vec{v}}{\Delta t}$$

Using the values we found:

$$\vec{a} = \frac{-60 \text{ m/s}}{0.010 \text{ s}}$$

To perform this calculation, divide -60 by 0.010:

$$\vec{a} = -6000 \text{ m/s}^2$$

The acceleration of the baseball during the impact is $-6000 \text{ m/s}^2$. The negative sign indicates that the acceleration is in the direction opposite to the initial velocity, which makes sense because the bat reverses the baseball's motion. This high value is typical for the acceleration during impact in sports like baseball.

This type of physics problem involving motion and forces is common in introductory physics. Understanding how to handle velocity change and impact time is key to solving such problems related to baseball acceleration.

Therefore, the baseball's acceleration during the impact is $-6000 \text{ m/s}^2$. This calculation helps us understand the forces involved in changing the baseball's motion so drastically in a short impact time.