Bus Acceleration Problem Overview

This problem asks us to determine the acceleration of a bus. Acceleration is a fundamental concept in physics, specifically in kinematics, which describes motion. Understanding how to calculate acceleration is key to analyzing how an object's speed changes over time.

Acceleration Concept Explained

Acceleration is defined as the rate at which the velocity of an object changes over time. When an object speeds up, slows down, or changes direction, it is accelerating. In this problem, the bus's speed is increasing, meaning it is undergoing positive acceleration.

• The formula used to calculate acceleration (\(a\)) is given by:
• \(a = \frac{\text{Change in velocity}}{\text{Time taken}}\)
• Which can be written as: \(a = \frac{v - u}{t}\)
• Where:
  • \(v\) is the final velocity (or final speed in this case, as motion is in a straight line).
  • \(u\) is the initial velocity (or initial speed).
  • \(t\) is the time taken for the change in velocity to occur.
• The standard unit for acceleration is meters per second squared (\(\text{m/s}^{2}\)).

Speed Values Provided for Bus

To calculate the bus's acceleration, we first need to identify the given values from the problem:

• Initial speed (\(u\)): The speed of the bus at the beginning of the observation.
• Final speed (\(v\)): The speed of the bus at the end of the observation.
• Time taken (\(t\)): The duration over which the speed change occurs.

Acceleration Calculation Steps

Now, let's substitute the given values into the acceleration formula and perform the calculation step-by-step.

• Step 1: Write down the acceleration formula.
• \(a = \frac{v - u}{t}\)
• Step 2: Substitute the known values into the formula.
• \(a = \frac{100 \text{ m/s} - 60 \text{ m/s}}{5 \text{ s}}\)
• Step 3: Calculate the change in velocity (numerator).
• \(100 \text{ m/s} - 60 \text{ m/s} = 40 \text{ m/s}\)
• So, the equation becomes: \(a = \frac{40 \text{ m/s}}{5 \text{ s}}\)
• Step 4: Perform the division to find the acceleration.
• \(a = 8 \text{ m/s}^{2}\)

Resulting Bus Acceleration

Based on our calculations, the acceleration of the bus is \(8 \text{ m/s}^{2}\). This means that for every second, the speed of the bus increases by 8 meters per second.