A Car Travels At 20 Km/h And Accelerates To 60 Km/h In 6 Seconds. What Is The Car's Acceleration?

In the realm of physics, acceleration is a fundamental concept that describes the rate at which an object's velocity changes over time. Understanding acceleration is crucial for comprehending the motion of objects around us, from cars on the road to planets in space. This article delves into the concept of acceleration, using a practical example of a car increasing its speed to illustrate the calculations and principles involved.

Defining Acceleration

At its core, acceleration is the measure of how quickly an object's velocity changes. Velocity, a vector quantity, encompasses both the speed and direction of an object's motion. Therefore, acceleration can occur due to a change in speed, a change in direction, or both. When an object speeds up, it experiences positive acceleration, while slowing down corresponds to negative acceleration, often referred to as deceleration. Constant velocity implies zero acceleration, as there is no change in either speed or direction. To quantify acceleration, we use the following formula:

Acceleration (a) = (Final Velocity (v) - Initial Velocity (u)) / Time (t)

This formula highlights that acceleration is directly proportional to the change in velocity and inversely proportional to the time interval over which the change occurs. The standard unit of acceleration in the International System of Units (SI) is meters per second squared (m/s²), which signifies the change in velocity (in meters per second) per second.

To truly grasp the concept, consider a scenario of a car initially moving at a speed of 20 km/h that increases its velocity to 60 km/h in a span of 6 seconds. This everyday example offers a tangible way to illustrate how we can apply the formula for acceleration to compute the car's rate of change in velocity. Understanding such calculations not only solidifies the theoretical understanding of the formula but also demonstrates its real-world applicability. By walking through the steps and converting the units, we begin to see how physical concepts like acceleration are not just abstract notions but are practical tools for measuring and describing the motion of objects in our daily lives. This connection between theory and application is what makes physics so compelling and relevant.

Problem Statement: Car Acceleration

Let's consider a specific scenario to illustrate the concept of acceleration. Imagine a car initially traveling at a speed of 20 kilometers per hour (km/h). This is the car's initial velocity. Over a period of 6 seconds, the driver accelerates, causing the car's speed to increase to 60 km/h. This final speed is the car's final velocity. Our objective is to determine the car's acceleration during this 6-second interval. This problem is a classic example of uniform acceleration, where the velocity changes at a constant rate. To solve this, we will use the formula for acceleration mentioned earlier. Before applying the formula, however, it's crucial to ensure that all the units are consistent. In physics, the standard unit for speed and velocity is meters per second (m/s), and the standard unit for time is seconds (s). Therefore, we need to convert the initial and final speeds from km/h to m/s. This conversion is a critical step because using inconsistent units can lead to incorrect results. Understanding the necessity of unit conversion is a fundamental aspect of problem-solving in physics. It highlights the importance of precision and attention to detail. Once we have converted the speeds to the correct units, we can then confidently plug the values into the acceleration formula and calculate the car's acceleration. This process not only gives us the numerical value of the acceleration but also reinforces the practical application of physics principles in real-world situations.

Step 1: Converting Units

Before we can calculate the acceleration, we need to ensure that all our units are consistent. The standard unit for velocity in physics is meters per second (m/s), while our problem provides the initial and final velocities in kilometers per hour (km/h). Therefore, we must convert km/h to m/s. To do this, we use the conversion factor:

1 km/h = (1000 meters) / (3600 seconds) = 5/18 m/s

Applying this conversion factor to the initial velocity (20 km/h):

Initial velocity (u) = 20 km/h * (5/18 m/s) = 5.56 m/s (approximately)

Similarly, for the final velocity (60 km/h):

Final velocity (v) = 60 km/h * (5/18 m/s) = 16.67 m/s (approximately)

Converting units is a crucial step in solving physics problems. It ensures that we are working with consistent measurements, which is essential for accurate calculations. Understanding how to convert between different units is a fundamental skill in physics and other scientific disciplines. In this case, we converted kilometers per hour to meters per second, but it's equally important to be able to convert between other units of length, time, and mass. The ability to perform unit conversions correctly is a cornerstone of problem-solving in physics, and mastering this skill will greatly enhance your ability to tackle a wide range of physics problems. Without proper unit conversion, the subsequent calculations would be meaningless, emphasizing the importance of this initial step.

Step 2: Applying the Acceleration Formula

Now that we have our initial velocity (u = 5.56 m/s), final velocity (v = 16.67 m/s), and the time interval (t = 6 s) in consistent units, we can apply the acceleration formula:

a = (v - u) / t

Substituting the values we have:

a = (16.67 m/s - 5.56 m/s) / 6 s

a = 11.11 m/s / 6 s

a = 1.85 m/s² (approximately)

This calculation shows that the car's acceleration is approximately 1.85 meters per second squared. The result is positive, which indicates that the car is accelerating, meaning its velocity is increasing over time. The unit m/s² signifies that the velocity of the car is increasing by 1.85 meters per second every second. This understanding of units is crucial for interpreting the physical meaning of the result. The acceleration formula is a fundamental concept in kinematics, the branch of physics that deals with the motion of objects. Applying this formula correctly, as we have done here, is a key step in solving many physics problems related to motion. Understanding how to substitute values into the formula and perform the calculations accurately is an essential skill for anyone studying physics. The result of our calculation not only provides a numerical answer but also gives us insights into the dynamics of the car's motion during the acceleration phase.

Result and Interpretation

Based on our calculations, the car's acceleration is approximately 1.85 m/s². This value tells us that the car's velocity increases by 1.85 meters per second every second during the 6-second interval. A positive acceleration value signifies that the car is speeding up, which aligns with the problem statement where the car's speed increases from 20 km/h to 60 km/h. In the context of driving, an acceleration of 1.85 m/s² is a moderate level of acceleration. It's enough to feel a noticeable change in speed but not so rapid as to be jarring or unsafe. Understanding acceleration is not just about performing calculations; it's also about interpreting what the result means in real-world scenarios. For example, a higher acceleration value would indicate a more rapid increase in speed, while a negative acceleration (deceleration) would indicate that the car is slowing down. The concept of acceleration is crucial in various fields beyond just physics. It's essential in engineering, where it's used to design vehicles and machines, and in sports science, where it's used to analyze the performance of athletes. By understanding the principles of acceleration, we can gain a deeper appreciation for how objects move and interact with each other in the world around us. The ability to calculate and interpret acceleration is a valuable skill that has numerous practical applications.

Key Takeaways

This exercise demonstrates the application of a fundamental physics concept—acceleration—to a real-world scenario. By calculating the acceleration of a car speeding up, we reinforce several key principles. First, understanding the definition of acceleration as the rate of change of velocity over time is crucial. Second, the importance of consistent units in physics calculations cannot be overstated. We saw how converting km/h to m/s was a necessary step to arrive at the correct answer. Third, the acceleration formula (a = (v - u) / t) is a powerful tool for quantifying changes in motion. Finally, interpreting the result within the context of the problem allows us to understand the physical meaning of the calculated value. In this case, the car's acceleration of 1.85 m/s² tells us how quickly its speed increased over the 6-second interval. These key takeaways are not just specific to this problem; they represent broader principles that apply to many areas of physics and engineering. The ability to analyze motion, perform unit conversions, and apply formulas correctly are essential skills for anyone studying or working in these fields. Furthermore, the ability to interpret results in a meaningful way is what bridges the gap between theoretical calculations and real-world understanding. By mastering these skills, we can tackle a wide range of problems and gain a deeper appreciation for the physical world around us. This example of calculating a car's acceleration serves as a valuable illustration of how physics concepts can be applied to everyday situations.