Certainly! Let's walk through the detailed, step-by-step solution to determine the final velocity of the bike.
Given:
- Initial velocity of the bike (\(u\)): \(10 \, \text{m/s}\)
- Acceleration (\(a\)): \(1.2 \, \text{m/s}^2\)
- Time (\(t\)): \(10 \, \text{s}\)
We need to calculate the final velocity (\(v\)) of the bike after 10 seconds of acceleration.
The formula to calculate the final velocity when an object is accelerating uniformly is:
[tex]\[ v = u + at \][/tex]
where:
- \(v\) is the final velocity
- \(u\) is the initial velocity
- \(a\) is the acceleration
- \(t\) is the time
Substituting the given values into the formula:
[tex]\[ v = 10 \, \text{m/s} + (1.2 \, \text{m/s}^2 \times 10 \, \text{s}) \][/tex]
Let's break it down:
1. First, calculate the product of the acceleration and the time:
[tex]\[ 1.2 \, \text{m/s}^2 \times 10 \, \text{s} = 12 \, \text{m/s} \][/tex]
2. Then, add this result to the initial velocity:
[tex]\[ v = 10 \, \text{m/s} + 12 \, \text{m/s} = 22 \, \text{m/s} \][/tex]
Therefore, the final velocity of the bike after 10 seconds is:
[tex]\[ \boxed{22 \, \text{m/s}} \][/tex]
