Calculating Acceleration A Car's Journey From Rest To 30 M/s In 12 Seconds

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In the realm of physics, understanding motion is fundamental, and acceleration plays a pivotal role in describing how an object's velocity changes over time. This article delves into a classic problem of uniformly accelerated motion: determining the acceleration of a car that starts from rest and reaches a velocity of 30 m/s in 12 seconds. We will explore the basic concepts, apply the relevant kinematic equation, and provide a step-by-step solution to this problem. Whether you are a student learning physics or simply curious about the science of motion, this discussion will offer valuable insights into the world of acceleration.

Acceleration, at its core, is the measure of how quickly an object's velocity changes. Velocity encompasses both the speed and direction of motion, so acceleration can result from changes in speed, direction, or both. It is a vector quantity, meaning it has both magnitude and direction. The standard unit of acceleration in the International System of Units (SI) is meters per second squared (m/s²). A positive value indicates acceleration in the direction of motion (speeding up), while a negative value indicates acceleration opposite to the direction of motion (slowing down, or deceleration).

Consider a car accelerating from a standstill. Initially, its velocity is zero, but as the driver presses the accelerator pedal, the car gains speed. This increase in velocity over time is acceleration. Similarly, when a car brakes, it decelerates, which is negative acceleration. The concept of acceleration is not limited to cars; it applies to any object in motion, from a ball rolling down a hill to a spaceship launching into orbit. Understanding acceleration is crucial in many fields, including engineering, sports science, and aerospace.

In our problem, we are dealing with uniform acceleration, which means that the acceleration remains constant over the given time interval. This simplifies our calculations as we can use standard kinematic equations. The car starts from rest, meaning its initial velocity is zero, and it reaches a final velocity of 30 m/s in 12 seconds. Our goal is to find the rate at which its velocity changed, which is the acceleration.

To solve this problem, we turn to one of the fundamental equations of kinematics, which describes the motion of objects under uniform acceleration. This equation relates the final velocity (v), initial velocity (u), acceleration (a), and time (t) as follows:

v = u + at

This equation is a cornerstone in the study of motion because it directly connects the variables we are interested in. It tells us that the final velocity of an object is the sum of its initial velocity and the product of its acceleration and the time interval over which the acceleration occurs. Understanding this equation is crucial for solving a wide range of physics problems involving constant acceleration.

In this specific scenario, we know the initial velocity (u), the final velocity (v), and the time (t), and we want to find the acceleration (a). Therefore, we need to rearrange the equation to solve for acceleration. By subtracting the initial velocity from both sides and then dividing by the time, we isolate acceleration and obtain the following formula:

a = (v - u) / t

This rearranged equation allows us to directly calculate the acceleration by plugging in the known values. It highlights the inverse relationship between acceleration and time: for a given change in velocity, a longer time interval implies a smaller acceleration, and vice versa. This equation is not just a mathematical tool; it provides a clear and intuitive understanding of how velocity changes over time under constant acceleration.

Now that we have the necessary equation, let's apply it to our problem step by step:

  1. Identify the given values:

    • Initial velocity (u) = 0 m/s (since the car starts from rest)
    • Final velocity (v) = 30 m/s
    • Time (t) = 12 seconds

  2. Write down the formula for acceleration:

    • a = (v - u) / t

  3. Substitute the given values into the formula:

    • a = (30 m/s - 0 m/s) / 12 s

  4. Perform the calculation:

    • a = 30 m/s / 12 s
    • a = 2.5 m/s²

Thus, the acceleration of the car is 2.5 meters per second squared. This means that the car's velocity increases by 2.5 meters per second every second. This step-by-step approach ensures clarity and reduces the chance of errors in the calculation. By first identifying the known values, selecting the appropriate formula, and then carefully substituting and calculating, we arrive at the correct answer. This methodical process is applicable to solving many physics problems.

After performing the calculations, we find that the acceleration of the car is 2.5 m/s². This value tells us the rate at which the car's velocity is changing. In simpler terms, for every second that passes, the car's speed increases by 2.5 meters per second. This is a uniform acceleration, meaning the rate of change in velocity remains constant throughout the 12-second interval.

An acceleration of 2.5 m/s² is a moderate acceleration in everyday terms. To put it into perspective, consider that a typical passenger car can accelerate from 0 to 60 mph (approximately 27 m/s) in around 8 to 10 seconds, which corresponds to an acceleration of about 2.7 to 3.4 m/s². Therefore, the car in our problem is accelerating at a rate that is within the typical range for passenger vehicles.

Understanding the magnitude and direction of acceleration is crucial in various applications. In automotive engineering, acceleration is a key performance metric. It determines how quickly a vehicle can reach a certain speed, which is essential for safety and efficiency. In sports, acceleration is vital in events like sprinting and race car driving, where quick changes in speed can make the difference between winning and losing. In physics education, problems like this serve as foundational examples for understanding more complex concepts in dynamics and mechanics.

In this article, we have explored a fundamental problem in physics: calculating the acceleration of a car that starts from rest and reaches a velocity of 30 m/s in 12 seconds. By understanding the concept of acceleration, applying the relevant kinematic equation (v = u + at), and following a step-by-step solution, we determined that the car's acceleration is 2.5 m/s². This problem serves as a valuable illustration of uniformly accelerated motion and highlights the importance of acceleration in understanding the motion of objects.

The ability to calculate acceleration is not just an academic exercise; it has practical applications in numerous fields. From designing safer vehicles to optimizing athletic performance, understanding how velocity changes over time is crucial. The principles we have discussed here form the basis for more advanced topics in physics and engineering, making this a fundamental concept for anyone interested in the science of motion. By mastering these basics, you can gain a deeper appreciation for the world around you and the physics that governs it.