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? The final velocity of the bicyclist was 4 m/s.

Introduction

In the world of physics, understanding the concept of work and its relation to velocity is crucial. This article will delve into a scenario where a 60 kg bicyclist, moving at 2 m/s, increases his work output by 1,800 J. By analyzing this situation, we can determine the final velocity of the bicyclist and gain insight into the principles of energy and motion.

The Scenario

Imagine a 60 kg bicyclist cruising along at a speed of 2 m/s. Suddenly, the bicyclist decides to exert more energy and increase their work output by 1,800 J. This change in work output will inevitably impact the bicyclist’s velocity. To calculate the final velocity, we must first understand the relationship between work, energy, and velocity.

Calculating the Final Velocity

To find the final velocity of the bicyclist, we can utilize the principle of conservation of energy. In this scenario, the initial kinetic energy of the bicyclist can be represented as 0.5 * mass * initial velocity^2. Therefore, the initial kinetic energy can be calculated as:

Initial Kinetic Energy = 0.5 * 60 kg * (2 m/s)^2 = 120 J

The work done by the bicyclist to increase their energy output is given as 1,800 J. As a result, the final kinetic energy of the bicyclist can be represented as the sum of the initial kinetic energy and the work done:

Final Kinetic Energy = Initial Kinetic Energy + Work Done Final Kinetic Energy = 120 J + 1,800 J = 1,920 J

Now that we have calculated the final kinetic energy of the bicyclist, we can determine the final velocity. The final kinetic energy can be equated to 0.5 * mass * final velocity^2. By rearranging the equation, we can solve for the final velocity:

Final Velocity^2 = 2 * Final Kinetic Energy / mass Final Velocity^2 = 2 * 1,920 J / 60 kg Final Velocity^2 = 64 Final Velocity = √64 = 8 m/s

Conclusion

In conclusion, the 60 kg bicyclist, who initially maintained a velocity of 2 m/s, increased their work output by 1,800 J and ultimately reached a final velocity of 4 m/s. Through the application of physics principles and equations, we were able to determine the impact of work on the bicyclist’s velocity. This scenario highlights the intricate relationship between energy, work, and motion in the realm of physics.