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’s Final Velocity Calculation

A 60 kg bicyclist going 2 m/s increased his work output by 1,800 J. What was his final velocity? Let’s break it down step by step to solve this problem efficiently.

Understanding the Concept of Work and Kinetic Energy

Before diving into the calculation, it is essential to grasp the fundamental concepts at play here. In this scenario, we are dealing with the work done by the bicyclist, which results in a change in kinetic energy.

Work: In physics, work is defined as the force applied to an object over a distance. It is calculated as the product of the force and the distance moved in the direction of that force. Kinetic Energy: Kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object is directly proportional to its mass and the square of its velocity.

Calculating the Initial Kinetic Energy

To determine the final velocity of the bicyclist, we first need to calculate the initial kinetic energy using the given information:

Initial Velocity (u): 2 m/s Mass (m): 60 kg

The formula to calculate kinetic energy is:

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

Substitute the values:

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

The initial kinetic energy of the bicyclist is 120 J.

Applying the WorkEnergy Principle

According to the workenergy principle, the work done on an object is equal to the change in its kinetic energy. In this case, the work output is given as 1,800 J.

The work done can be calculated as follows:

\[ W = KE\_final KE\_initial \] \[ KE\_final = W + KE\_initial \] \[ KE\_final = 1,800 + 120 = 1,920 J \]

Finding the Final Velocity

Now that we have determined the final kinetic energy, we can calculate the final velocity using the same formula as before:

\[ KE = \frac{1}{2}mv^2 \] \[ 1,920 = \frac{1}{2} \times 60 \times v^2 \] \[ 1,920 = 30v^2 \] \[ v^2 = \frac{1,920}{30} = 64 \] \[ v = \sqrt{64} = 8 \text{ m/s} \]

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

Final Thoughts

By understanding the principles of work, kinetic energy, and their relationship, we were able to calculate the final velocity of the bicyclist accurately. This problem highlights the practical application of physics concepts in realworld scenarios, showcasing the significance of a strong foundation in fundamental principles.