A pitcher requires about \(0.2\) second to throw a baseball. If the ball leaves his hand with a velocity of \(80 \mathrm{~m} / \mathrm{s}\), what is its acceleration? A. \(40 \mathrm{~m} / \mathrm{s}^2\) B. \(400 \mathrm{~m} / \mathrm{s}^2\) C. \(40 \mathrm{~m} / \mathrm{s}\) D. \(4 \mathrm{~m} / \mathrm{s}\)

Physics problem solving often involves breaking a problem down into smaller steps. This method helps you focus on one part of the problem at a time. Start by identifying the given information and what you need to find.

In our example problem, the pitcher takes about 0.2 seconds to throw the baseball, and the ball leaves his hand with a velocity of 80 m/s. The question asks us to find the acceleration.

Next, understand which formulas apply to the situation. Here, you need the acceleration formula, which relates the change in velocity to the change in time. Applying the formula with the given data, you can methodically work your way to the solution.

Following a step-by-step approach not only simplifies the problem but also minimizes the potential for errors. Learn to practice this method regularly, and you’ll find yourself more confident in solving physics problems.

The relationship between velocity and time is crucial for understanding motion. Velocity is simply the speed of an object in a particular direction, typically measured in meters per second (m/s).

In this problem, the baseball reaches a velocity of 80 m/s in 0.2 seconds. By knowing how quickly the velocity changes, we can find the acceleration.

This relationship is important because it helps you connect how fast something is moving and how long it takes to reach that speed. If an object reaches a high velocity quickly, the acceleration must be large. Conversely, if it takes a long time to reach a certain speed, the acceleration will be smaller.

Understanding this concept helps in visualizing how objects move in real life, be it a car accelerating on a highway or a ball being pitched in a game.

The acceleration formula is essential for solving many physics problems related to motion. Acceleration (\(a\)) is defined as the rate of change of velocity (\(\Delta v\)) with respect to time (\(\Delta t\)). The formula is written as:

\[ a = \frac{\text{Change in Velocity } (\triangle v)}{\text{Change in Time } (\triangle t)} \]
Given in our problem, \(\Delta v = 80 \, \text{m/s}\) and \(\Delta t = 0.2 \, \text{s}\). Substitute these values into the formula:

\[ a = \frac{80 \, \text{m/s}}{0.2 \, \text{s}} = 400 \, \text{m/s}^2 \]

The calculated acceleration comes out to be 400 \(\text{m/s}^2\).

This is a powerful technique – use the formula to turn what you know into what you need to find. The key is to clearly identify the initial and final velocities and the time duration of the motion. Substitute these values carefully into the formula, and simplify to find the acceleration.

Mastering this application will allow you to solve a wide range of problems involving motion, whether it’s calculating acceleration, velocity, or other aspects of moving objects.