Understanding Car Acceleration: Converting Velocity and Calculating Acceleration

Introduction

Accelerating a car from rest to a desired speed is a fundamental aspect of automotive dynamics. In this guide, we will focus on the specific scenario where a car starts from rest and reaches a velocity of 108 km/hr in 60 seconds. We will outline the process of converting velocity units and calculating the car's acceleration using basic equations of motion.

Basic Concepts of Acceleration and Velocity Conversion

In physics, acceleration is defined as the change in velocity per unit of time. The SI unit of acceleration is meters per second squared (m/s2). To solve problems involving velocity and time, it's crucial to ensure that all units are consistent.

Conversion of Units

Let's start with the given velocity and time:

Given Data

Initial Velocity, u 0 m/s Final Velocity, v 108 km/hr Time, t 60 seconds

Step 1: Convert Velocity Units from km/hr to m/s

To convert 108 km/hr to m/s, we use the conversion factors:

108 , text{km/hr} 108 times frac{1000 , text{m}}{1 , text{km}} times frac{1 , text{hr}}{3600 , text{s}} 108 times frac{1000}{3600}, text{m/s} 30 , text{m/s}

Step 2: Calculate Acceleration using the SUVAT Formula

The SUVAT equation for speed is:

v u at

Given:

v 30 , text{m/s}, , u 0 , text{m/s}, , text{and} , t 60 , text{s}

Solving for acceleration, a:

a frac{var{v} - var{u}}{var{t}} frac{30 , text{m/s} - 0 , text{m/s}}{60 , text{s}} 0.5 , text{m/s}^2

Explanation and Alternative Solutions

Alternatively, you can use the SUVAT equation for distance:

x ut frac{1}{2}at2

Since the car starts from rest, we can simplify the equation to:

frac{1}{2}at2end{math>

Solving for acceleration, we get:

a frac{2var{x}}{var{t}2} frac{2 times 108000 , text{m}}{(60 , text{s})^2} 0.5 , text{m/s}^2

Conclusion

By following these steps, you can effectively convert velocity units and compute acceleration. The key is to ensure that all units are consistent and to use the appropriate formulas based on the given data.

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