Answer :
Certainly! Let's solve the problem step-by-step to determine the final velocity of the object.
### Given Data:
- Initial velocity (\( u \)) = 0 m/s (since the object starts from rest)
- Acceleration (\( a \)) = 2 m/s\(^2\)
- Distance (\( s \)) = 20 m
### Kinematic Equation:
To find the final velocity (\( v \)), we can use the kinematic equation:
[tex]\[ v^2 = u^2 + 2as \][/tex]
where:
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( s \) is the distance.
### Step-by-Step Solution:
1. Substitute the known values into the kinematic equation:
[tex]\[ v^2 = 0^2 + 2 \times 2 \, \text{m/s}^2 \times 20 \, \text{m} \][/tex]
2. Simplify the equation:
[tex]\[ v^2 = 0 + 2 \times 2 \times 20 \][/tex]
[tex]\[ v^2 = 80 \][/tex]
3. Solve for \( v \) by taking the square root of both sides:
[tex]\[ v = \sqrt{80} \][/tex]
4. Approximate the result:
[tex]\[ v \approx 8.944 \, \text{m/s} \][/tex]
### Conclusion:
The final velocity of the object, after accelerating at a rate of 2 m/s² over a distance of 20 meters, is approximately 8.944 m/s.
### Given Data:
- Initial velocity (\( u \)) = 0 m/s (since the object starts from rest)
- Acceleration (\( a \)) = 2 m/s\(^2\)
- Distance (\( s \)) = 20 m
### Kinematic Equation:
To find the final velocity (\( v \)), we can use the kinematic equation:
[tex]\[ v^2 = u^2 + 2as \][/tex]
where:
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( s \) is the distance.
### Step-by-Step Solution:
1. Substitute the known values into the kinematic equation:
[tex]\[ v^2 = 0^2 + 2 \times 2 \, \text{m/s}^2 \times 20 \, \text{m} \][/tex]
2. Simplify the equation:
[tex]\[ v^2 = 0 + 2 \times 2 \times 20 \][/tex]
[tex]\[ v^2 = 80 \][/tex]
3. Solve for \( v \) by taking the square root of both sides:
[tex]\[ v = \sqrt{80} \][/tex]
4. Approximate the result:
[tex]\[ v \approx 8.944 \, \text{m/s} \][/tex]
### Conclusion:
The final velocity of the object, after accelerating at a rate of 2 m/s² over a distance of 20 meters, is approximately 8.944 m/s.
