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? m/s

Calculating the Final Velocity

To determine the final velocity of the bicyclist after increasing his work output by 1,800 J, we can utilize the principle of conservation of energy. The work done on an object is equal to the change in its kinetic energy. The initial kinetic energy (KE) of the bicyclist can be calculated using the formula:

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

where \(m\) is the mass of the bicyclist (60 kg) and \(v\) is his initial velocity (2 m/s). Substituting the values, we get:

\[ KE{initial} = \frac{1}{2} \times 60 \times (2)^2 \] \[ KE{initial} = \frac{1}{2} \times 60 \times 4 \] \[ KE_{initial} = 120 J \]

The work done on the bicyclist is given as 1,800 J. According to the conservation of energy, this work done on the cyclist will result in an increase in kinetic energy, leading to a final velocity. The change in kinetic energy (\(ΔKE\)) can be calculated as:

\[ ΔKE = Work \ done \] \[ KE{final} KE{initial} = 1,800 J \] \[ KE{final} 120 = 1,800 J \] \[ KE{final} = 1,800 J + 120 J \] \[ KE_{final} = 1,920 J \]

The final kinetic energy can be related to the final velocity of the bicyclist using the same formula:

\[ KE_{final} = \frac{1}{2}mv_f^2 \]

where \(v_f\) is the final velocity we are looking for. Rearranging the formula, we get:

\[ vf = \sqrt{\frac{2 \times KE{final}}{m}} \] \[ v_f = \sqrt{\frac{2 \times 1,920}{60}} \] \[ v_f = \sqrt{\frac{3,840}{60}} \] \[ v_f = \sqrt{64} \] \[ v_f = 8 \ m/s \]

Therefore, the final velocity of the 60 kg bicyclist after increasing his work output by 1,800 J is 8 m/s.

Conclusion

In conclusion, by applying the principle of conservation of energy and utilizing the formula for kinetic energy, we were able to calculate the final velocity of the bicyclist. The increase in work output resulted in an increase in kinetic energy, leading to a final velocity of 8 m/s. This calculation showcases the relationship between work, energy, and velocity in the context of a moving object like a bicyclist.