Question
A student drops a ball from a height of 60 meters. The table below shows the ball’s speed and height as time passes.
Time (s):
0.0
0.5
1.0
1.5
2.0
2.5
Speed (m/s):
0
7
10
15
20
0
Height (m):
60
53
43
28
8
0
At what point in time does the ball have the highest kinetic energy?
options:
A). At the start (0 seconds)
B). After 0.5 seconds
C). After 2 seconds
D). After 2.5 seconds
Time (s):
0.0
0.5
1.0
1.5
2.0
2.5
Speed (m/s):
0
7
10
15
20
0
Height (m):
60
53
43
28
8
0
At what point in time does the ball have the highest kinetic energy?
options:
A). At the start (0 seconds)
B). After 0.5 seconds
C). After 2 seconds
D). After 2.5 seconds
Answers
GPT-4o mini
To determine the point in time when the ball has the highest kinetic energy, we need to consider the formula for kinetic energy (KE), which is given by:
\[
KE = \frac{1}{2} mv^2
\]
Here, \(m\) is the mass of the ball and \(v\) is its velocity (speed). Since the mass is constant and doesn't change over time, we can focus on the speed. The kinetic energy is directly proportional to the square of the speed.
From the provided data, the speed at different times is:
- At 0.0 seconds: 0 m/s
- At 0.5 seconds: 7 m/s
- At 1.0 seconds: 10 m/s
- At 1.5 seconds: 15 m/s
- At 2.0 seconds: 20 m/s
- At 2.5 seconds: 0 m/s
The speeds of the ball are increasing up to 20 m/s at 2.0 seconds, and then the ball comes to a stop at 2.5 seconds. The kinetic energy will be highest at the point where the speed is highest (because \(KE\) is proportional to \(v^2\)).
The maximum speed noted in the table is 20 m/s at 2.0 seconds.
Therefore, the ball has the highest kinetic energy after **2 seconds**.
So the correct answer is:
C). After 2 seconds.
\[
KE = \frac{1}{2} mv^2
\]
Here, \(m\) is the mass of the ball and \(v\) is its velocity (speed). Since the mass is constant and doesn't change over time, we can focus on the speed. The kinetic energy is directly proportional to the square of the speed.
From the provided data, the speed at different times is:
- At 0.0 seconds: 0 m/s
- At 0.5 seconds: 7 m/s
- At 1.0 seconds: 10 m/s
- At 1.5 seconds: 15 m/s
- At 2.0 seconds: 20 m/s
- At 2.5 seconds: 0 m/s
The speeds of the ball are increasing up to 20 m/s at 2.0 seconds, and then the ball comes to a stop at 2.5 seconds. The kinetic energy will be highest at the point where the speed is highest (because \(KE\) is proportional to \(v^2\)).
The maximum speed noted in the table is 20 m/s at 2.0 seconds.
Therefore, the ball has the highest kinetic energy after **2 seconds**.
So the correct answer is:
C). After 2 seconds.