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The table shows the speed and height over time of a ball that starts at rest, then is dropped from the top of a building, which is 60 meters (m) tall.

 

SPEED AND HEIGHT OVER TIME
Time (s) Speed (m/s) Height (m)
0.0 0 60
0.5 7 53
1.0 10 43
1.5 15 28
2.0 20 8
2.5 0 0

After how many seconds is the ball's kinetic energy at its maximum?

1 answer

The kinetic energy of an object is calculated using the formula:

\[ KE = \frac{1}{2}mv^2 \]

where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is its speed.

In this case, the mass \( m \) is constant, so the kinetic energy will be maximized when the speed \( v \) is at its maximum. The table shows the speed of the ball at different times:

  • At 0.0 seconds: Speed = 0 m/s
  • At 0.5 seconds: Speed = 7 m/s
  • At 1.0 seconds: Speed = 10 m/s
  • At 1.5 seconds: Speed = 15 m/s
  • At 2.0 seconds: Speed = 20 m/s
  • At 2.5 seconds: Speed = 0 m/s (the ball has hit the ground)

From the data, the speed of the ball continues to increase until it reaches a maximum speed of 20 m/s at 2.0 seconds. After this point, the ball begins to decelerate until it comes to a stop at 2.5 seconds.

Thus, the ball's kinetic energy is at its maximum at approximately 2.0 seconds.