Question
A skydiver jumps outs of a plane and begins to accelerate his speed increasing to 20 m/s then 30 m/s his acceleration slows until he reaches a constant speed of 50 m/s Which statement accurately describes his connect energy while falling A his kinetic energy increases while his speed increases then it became constant B his kinetic energy increased quickly at first then it's increased at a constant rate C his kinetic energy would remain the same for the whole fall as he long as he lost no mass D his kinetic energy was positive at first but it decreased to zero when he stopped accelerating
Answers
GPT-4o mini
To analyze the kinetic energy of the skydiver during the fall, we can use the formula for kinetic energy, which is:
\[
KE = \frac{1}{2} m v^2
\]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the skydiver, and
- \( v \) is the velocity.
1. As the skydiver accelerates, his velocity \( v \) increases. Since kinetic energy is proportional to the square of velocity, as his speed increases from 20 m/s to 30 m/s and then stabilizes at 50 m/s, his kinetic energy will also increase.
2. Once he reaches a constant speed of 50 m/s, his kinetic energy remains constant as long as his mass does not change.
3. Based on these points, let's evaluate the given options:
- **A. His kinetic energy increases while his speed increases; then it became constant.**
This statement accurately describes the situation. Kinetic energy increases with the increase in speed and remains constant when speed becomes constant.
- **B. His kinetic energy increased quickly at first; then it increased at a constant rate.**
This is not entirely accurate because while the kinetic energy increases with speed, it does not increase at a constant rate due to the quadratic relationship between speed and kinetic energy.
- **C. His kinetic energy would remain the same for the whole fall as long as he lost no mass.**
This is incorrect because kinetic energy does change during the fall (it increases) until he reaches terminal velocity.
- **D. His kinetic energy was positive at first, but it decreased to zero when he stopped accelerating.**
This statement is also incorrect because although he may stop accelerating, his kinetic energy does not go to zero; it remains constant at the value corresponding to his constant speed.
Thus, the most accurate statement is:
**A. His kinetic energy increases while his speed increases; then it became constant.**
\[
KE = \frac{1}{2} m v^2
\]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the skydiver, and
- \( v \) is the velocity.
1. As the skydiver accelerates, his velocity \( v \) increases. Since kinetic energy is proportional to the square of velocity, as his speed increases from 20 m/s to 30 m/s and then stabilizes at 50 m/s, his kinetic energy will also increase.
2. Once he reaches a constant speed of 50 m/s, his kinetic energy remains constant as long as his mass does not change.
3. Based on these points, let's evaluate the given options:
- **A. His kinetic energy increases while his speed increases; then it became constant.**
This statement accurately describes the situation. Kinetic energy increases with the increase in speed and remains constant when speed becomes constant.
- **B. His kinetic energy increased quickly at first; then it increased at a constant rate.**
This is not entirely accurate because while the kinetic energy increases with speed, it does not increase at a constant rate due to the quadratic relationship between speed and kinetic energy.
- **C. His kinetic energy would remain the same for the whole fall as long as he lost no mass.**
This is incorrect because kinetic energy does change during the fall (it increases) until he reaches terminal velocity.
- **D. His kinetic energy was positive at first, but it decreased to zero when he stopped accelerating.**
This statement is also incorrect because although he may stop accelerating, his kinetic energy does not go to zero; it remains constant at the value corresponding to his constant speed.
Thus, the most accurate statement is:
**A. His kinetic energy increases while his speed increases; then it became constant.**