Answer :
To find out how fast the 128-kg object was initially moving, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
Here's a step-by-step explanation:
1. Understand the Work-Energy Principle:
The work done on an object is equal to the change in its kinetic energy. Since the object is brought to a stop, its final kinetic energy is zero. Therefore, the initial kinetic energy is equal to the work done on the object.
2. Formula for Kinetic Energy:
The formula for kinetic energy ([tex]\( KE \)[/tex]) is:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times (\text{velocity})^2 \][/tex]
3. Set Up the Equation:
From the work-energy principle, we have:
[tex]\[ \frac{1}{2} \times \text{mass} \times (\text{velocity})^2 = \text{work done} \][/tex]
Here, the mass of the object is 128 kg, and the work done is 60000 J (Joules).
4. Rearrange the Equation to Solve for Velocity:
[tex]\[\frac{1}{2} \times 128 \times (\text{velocity})^2 = 60000\][/tex]
5. Isolate [tex]\((\text{velocity})^2\)[/tex]:
[tex]\[(\text{velocity})^2 = \frac{2 \times 60000}{128}\][/tex]
6. Calculate [tex]\((\text{velocity})^2\)[/tex]:
[tex]\[(\text{velocity})^2 = 937.5\][/tex]
7. Find the Velocity:
To find the velocity, take the square root of 937.5:
[tex]\[\text{velocity} = \sqrt{937.5} \approx 30.62 \, \text{m/s}\][/tex]
Therefore, the object was initially moving at a speed of approximately 30.62 meters per second.
Here's a step-by-step explanation:
1. Understand the Work-Energy Principle:
The work done on an object is equal to the change in its kinetic energy. Since the object is brought to a stop, its final kinetic energy is zero. Therefore, the initial kinetic energy is equal to the work done on the object.
2. Formula for Kinetic Energy:
The formula for kinetic energy ([tex]\( KE \)[/tex]) is:
[tex]\[ KE = \frac{1}{2} \times \text{mass} \times (\text{velocity})^2 \][/tex]
3. Set Up the Equation:
From the work-energy principle, we have:
[tex]\[ \frac{1}{2} \times \text{mass} \times (\text{velocity})^2 = \text{work done} \][/tex]
Here, the mass of the object is 128 kg, and the work done is 60000 J (Joules).
4. Rearrange the Equation to Solve for Velocity:
[tex]\[\frac{1}{2} \times 128 \times (\text{velocity})^2 = 60000\][/tex]
5. Isolate [tex]\((\text{velocity})^2\)[/tex]:
[tex]\[(\text{velocity})^2 = \frac{2 \times 60000}{128}\][/tex]
6. Calculate [tex]\((\text{velocity})^2\)[/tex]:
[tex]\[(\text{velocity})^2 = 937.5\][/tex]
7. Find the Velocity:
To find the velocity, take the square root of 937.5:
[tex]\[\text{velocity} = \sqrt{937.5} \approx 30.62 \, \text{m/s}\][/tex]
Therefore, the object was initially moving at a speed of approximately 30.62 meters per second.
