a 60 kg bicyclist going 2 m/s increased his work output by 1,800 j. what was his final velocity? m/s

A 60 kg bicyclist going 2 m/s increased his work output by 1,800 J. What was his final velocity in m/s?

Calculating the Final Velocity

To calculate the final velocity of the bicyclist, we can use the workenergy principle. The workenergy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the bicyclist is equal to the change in his kinetic energy.

Given Variables:

Mass (m) = 60 kg Initial Velocity (u) = 2 m/s Work Output (W) = 1,800 J

Calculating the Initial Kinetic Energy (KEi):

The initial kinetic energy of the bicyclist can be calculated using the formula:

KEi = 0.5 * m * u^2

Plugging in the values:

KEi = 0.5 * 60 kg * (2 m/s)^2 KEi = 0.5 * 60 kg * 4 m^2/s^2 KEi = 120 J

Calculating the Final Kinetic Energy (KEf):

The final kinetic energy of the bicyclist can be calculated using the formula:

KEf = KEi + W

Plugging in the values:

KEf = 120 J + 1,800 J KEf = 1,920 J

Calculating the Final Velocity (v):

The final velocity of the bicyclist can be calculated using the formula for kinetic energy:

KEf = 0.5 * m * v^2

Rearranging the formula to solve for velocity:

v = sqrt((2 * KEf) / m)

Plugging in the values:

v = sqrt((2 * 1,920 J) / 60 kg) v = sqrt(3,840 J / 60 kg) v = sqrt(64 m^2/s^2) v = 8 m/s

Therefore, the final velocity of the bicyclist is 8 m/s.