Automobile Velocity After Acceleration: Solved Physics Problem

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Hey guys! Let's break down this classic physics problem together, step by step. We're dealing with a car that's accelerating, and we need to figure out its final velocity after a certain amount of time. It might sound tricky, but don't worry – we'll get through it! This is one of those problems that really helps solidify your understanding of kinematics, which is a fundamental part of physics. Understanding these concepts is super important, not just for exams, but also for grasping how the world around us works. So, let's dive in and see how we can solve this problem using the principles of physics.

Problem Statement

Let's start by restating the problem in a clear and straightforward way:

A car starts with an initial velocity of 10 m/s and accelerates uniformly at a rate of 2 m/s². What will its velocity be after 5 seconds?

We have a few answer options to choose from:

a) 20 m/s b) 30 m/s c) 25 m/s d) 15 m/s

To solve this, we'll need to use some physics formulas, but more importantly, we need to understand what's happening in the problem. The car is speeding up at a constant rate, and we want to know how fast it will be going after 5 seconds. Let's get into the nitty-gritty of how to solve this.

Identifying Key Information

Before we jump into calculations, it's crucial to identify the key pieces of information given in the problem. This is like gathering our tools before starting a job. So, what do we know?

  • Initial Velocity (vâ‚€): 10 m/s. This is the speed the car is traveling at when we start observing it.
  • Acceleration (a): 2 m/s². This tells us how much the car's velocity increases each second. It's a constant, meaning the car speeds up at the same rate throughout the 5 seconds.
  • Time (t): 5 seconds. This is the duration over which the car accelerates.
  • Final Velocity (v): This is what we want to find – the car's speed after 5 seconds of acceleration.

Now that we have all the pieces of the puzzle, we can start thinking about how to put them together. The next step is to choose the right formula that connects these variables.

Choosing the Right Formula

Okay, so we know what we're given and what we need to find. The next step is figuring out which physics equation will help us connect all the pieces. In this case, we're dealing with uniform acceleration, meaning the acceleration is constant. This is key because it allows us to use one of the fundamental kinematic equations. The equation that fits perfectly is:

v = vâ‚€ + at

Where:

  • v is the final velocity
  • vâ‚€ is the initial velocity
  • a is the acceleration
  • t is the time

This equation is like a Swiss Army knife for constant acceleration problems. It directly relates initial velocity, acceleration, time, and final velocity. Now, let's see how we can plug in our known values and solve for the unknown.

Applying the Formula and Solving

Alright, we've got our formula, and we've identified all the values. Now comes the fun part – plugging in the numbers and solving for the final velocity! Let's take it step by step:

  1. Write down the formula: v = vâ‚€ + at

  2. Substitute the known values:

    • vâ‚€ = 10 m/s
    • a = 2 m/s²
    • t = 5 s

    So, our equation becomes:

    v = 10 m/s + (2 m/s²)(5 s)

  3. Perform the calculation:

    v = 10 m/s + 10 m/s v = 20 m/s

So, after 5 seconds, the car's velocity will be 20 m/s. That wasn't so bad, was it? Now, let's see which of the answer options matches our result.

Checking the Answer Options

We've calculated that the final velocity of the car after 5 seconds is 20 m/s. Now, let's go back to the answer options and see which one matches our result:

a) 20 m/s b) 30 m/s c) 25 m/s d) 15 m/s

It's clear that option a) 20 m/s is the correct answer. We've successfully solved the problem! But it's always a good idea to take a moment and think about whether our answer makes sense in the context of the problem. Does 20 m/s seem like a reasonable final velocity given the initial conditions and the acceleration?

Does the Answer Make Sense?

Let's take a step back and think about whether our answer makes sense in the real world. This is a crucial part of problem-solving in physics – it's not just about getting the right number, but also understanding what that number means.

  • The car started at 10 m/s.
  • It accelerated at 2 m/s² for 5 seconds.

This means that each second, the car's speed increased by 2 m/s. Over 5 seconds, the total increase in speed would be:

(2 m/s²) * (5 s) = 10 m/s

Adding this increase to the initial velocity:

10 m/s (initial) + 10 m/s (increase) = 20 m/s

Our calculated final velocity of 20 m/s aligns perfectly with this reasoning. It makes sense that the car, starting at 10 m/s and accelerating, would reach 20 m/s after 5 seconds. This step of checking for reasonableness is super important – it can help you catch mistakes and build a better understanding of the physics involved.

Final Answer and Explanation

So, to wrap things up, the final answer to the problem is:

a) 20 m/s

Here's a quick recap of how we got there:

  1. We identified the key information: initial velocity (10 m/s), acceleration (2 m/s²), and time (5 s).
  2. We chose the appropriate kinematic equation: v = vâ‚€ + at.
  3. We plugged in the values and calculated the final velocity: v = 20 m/s.
  4. We checked our answer to make sure it made sense in the context of the problem.

By breaking down the problem into smaller steps and understanding the underlying physics, we were able to solve it confidently. Remember, physics problems aren't just about formulas – they're about understanding how the world works! Keep practicing, and you'll become a pro at these in no time!

Practice Problems

To really nail down these concepts, it's super helpful to practice with similar problems. Here are a couple you can try on your own:

  1. A train starts from rest and accelerates uniformly at 1.5 m/s² for 10 seconds. What is its final velocity?
  2. A cyclist is traveling at 5 m/s and accelerates at 0.8 m/s² for 6 seconds. What is their final velocity?

Try solving these using the same steps we used in this article. Don't just focus on getting the right answer – make sure you understand why you're doing each step. This will help you build a solid foundation in physics and tackle more challenging problems in the future. And hey, if you get stuck, don't hesitate to look back at this guide or reach out to a friend or teacher for help. We're all in this together!