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 and His Final Velocity

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

Calculation of Final Velocity

To find the final velocity of the 60 kg bicyclist after increasing his work output by 1,800 J, we can utilize the principle of conservation of energy.

Initial kinetic energy (KE) of the bicyclist: Formula: KE = 0.5 * m * v^2 Given: m = 60 kg, v = 2 m/s Calculation: KE = 0.5 * 60 kg * (2 m/s)^2 Result: KE = 120 J

Total work done on the bicyclist: Given: Work = 1,800 J

Final kinetic energy of the bicyclist: Considering that work done = change in KE Work = KE_final KE_initial Substituting values and rearranging: 1,800 J = KE_final 120 J KE_final = 1,920 J

Final velocity calculation: Formula: KE = 0.5 * m * v^2 Substituting values: 1,920 J = 0.5 * 60 kg * v_final^2 v_final^2 = 64 m^2/s^2 v_final = √64 m/s v_final = 8 m/s

Conclusion

After increasing his work output by 1,800 J, the final velocity of the 60 kg bicyclist would be 8 m/s.

By following the conservation of energy principle and understanding the relationship between work, kinetic energy, and velocity, we were able to determine the final velocity of the bicyclist accurately.

In essence, the bicyclist’s increased work input translated into a substantial boost in kinetic energy, propelling him to a higher final velocity of 8 m/s compared to his initial speed of 2 m/s.

In this scenario, the synergy between the applied work and the bicyclist’s mass exemplifies how energy transformations lead to tangible changes in velocity, showcasing the fundamental principles of physics in action.