Understanding Acceleration and Distance Calculation in a Real-World Scenario

In everyday situations, we often encounter instances where objects change their velocity over a given time. One such real-world example is a truck traveling at a constant speed that then applies the brakes and comes to a complete stop. This scenario involves calculations of acceleration and distance traveled. Let's break down the problem step by step to understand the underlying physics concepts.

Problem Statement

A truck is traveling at a velocity of 12 meters per second (m/s) and then applies the brakes, coming to a complete stop after 1.25 seconds. We need to calculate the acceleration and the distance traveled during this braking process.

Calculating Acceleration

First, let's calculate the acceleration.

The formula for acceleration is:

a#124;v-u#124;#948;t;v is the final velocity, u is the initial velocity, and #948;t is the time interval.

Given:

Initial velocity, ( u 12 , text{m/s} ) Final velocity, ( v 0 , text{m/s} ) Time, ( Delta t 1.25 , text{s} )

Substituting the values into the formula:

a#124;v-u#124;#948;t#124;0-12#124;1.25121.25-9.6 m/s2

The negative sign indicates deceleration or retardation, as the velocity is decreasing.

Calculating Distance Traveled

Next, let's calculate the distance traveled during the braking process. We can use the formula:

du v2#948;t

First, we calculate the average velocity:

v_{avg}u v212 026 , text{m/s}

Now, using the average velocity to find the distance traveled:

dv_{avg}#948;t6#948;1.257.5 , text{meters}

Therefore, the truck travels a distance of 7.5 meters before coming to a complete stop.

Conclusion

The problem demonstrates the application of basic physics principles to real-world scenarios. Understanding acceleration and distance in such situations can be crucial in fields like automotive engineering, transportation science, and traffic safety. The key concepts—the formulas for acceleration and distance traveled during a uniform deceleration process—are fundamental and widely applicable.

Keywords: acceleration, deceleration, distance traveled