Suppose you read about a new car that can go from 0 to \(100 \mathrm{km} / \mathrm{h}\) in only 2.0 seconds. What is this car's acceleration? a. about \(50 \mathrm{km} / \mathrm{h}\) b. about \(14 \mathrm{m} / \mathrm{s}^{2}\) c. about \(50 \mathrm{km} / \mathrm{s}^{2}\) d. about \(200 \mathrm{km}\) e. about \(0.056 \mathrm{km} / \mathrm{h}^{2}\)

Understanding the concept of acceleration is key in physics, especially when studying motion. Acceleration describes how quickly an object speeds up or slows down. It's a vector quantity, meaning it has both a magnitude and a direction. In practical terms, when you press the gas pedal of a car, you're experiencing acceleration. Newton's Second Law of Motion states that the force on an object is equal to its mass times its acceleration: \( F = ma \).Understanding acceleration helps in predicting how quickly an object can move from a state of rest, or how it can reach a specific speed in a given time.

Unit conversion is essential when solving physics problems, as it ensures we are using consistent units for all calculations. In the given exercise, we converted the speed from kilometers per hour (km/h) to meters per second (m/s). This makes calculations easier and more accurate. To convert km/h to m/s:
Multiply by 1000 to convert kilometers to meters.
Then divide by 3600 to convert hours to seconds. This is because there are 1000 meters in a kilometer and 3600 seconds in an hour. So, 100 km/h becomes approximately 27.78 m/s:
\( 100 \times \frac{1000}{3600} = 27.78 \text{ m/s} \).Different units are often used for different types of measurements due to convenience or convention, so mastering unit conversion is a valuable skill.

To calculate acceleration, we use one of the basic motion equations in physics:
and \text{Acceleration} \( a = \frac{\text{change in velocity}}{\text{time}} \) Given the final speed (27.78 m/s), initial speed (0 m/s), and time (2.0 s), we substitute these values into the formula: \( a = \frac{27.78 \text{ m/s} - 0 \text{ m/s}}{2.0 \text{ s}} = 13.89 \text{ m/s}^2 \).
This equation simplifies the process of determining how quickly an object's speed is changing. By understanding and applying motion equations, students can solve various real-world problems related to motion, such as calculating distances, speeds, and accelerations.
Recognizing these fundamental principles empowers students to tackle more complex physics problems with confidence.