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?

When faced with the task of determining the final velocity of a 60 kg bicyclist who initially travels at 2 m/s and increases his work output by 1,800 Joules, various factors come into play. Understanding the principles of work, energy, and velocity is crucial in unraveling this physics puzzle.

Work and Energy Relationship

Work Done: In physics, work is defined as the force applied over a distance. Mathematically, work (W) is represented as the product of force (F) and displacement (d) in the direction of the force. Therefore, the work done by the bicyclist can be calculated using the formula: \[W = F \cdot d \] where W is work done in Joules (J), F is force in Newtons (N), and d is displacement in meters (m).

Energy Change: Work done on an object results in a change in energy. In this case, the bicyclist’s work output of 1,800 J indicates an increase in his energy due to the applied force.

Kinetic Energy and Velocity

Kinetic Energy Equation: The total energy possessed by an object in motion is known as kinetic energy. For an object with mass (m) and velocity (v), kinetic energy (KE) can be calculated using the formula: \[ KE = \frac{1}{2} m \cdot v^2 \] where KE is in Joules (J), mass (m) in kilograms (kg), and velocity (v) in meters per second (m/s).

Conservation of Energy: When considering the initial and final states of the bicyclist’s motion, the principle of conservation of energy can be applied. This states that the total energy in an isolated system remains constant.

Solving for Final Velocity

To determine the final velocity of the 60 kg bicyclist after increasing his work output by 1,800 J, the following steps need to be taken:

1. Initial State:

Mass (m) = 60 kg Initial Velocity (v_i) = 2 m/s Initial Kinetic Energy (KE_i) = ? (to be calculated)

1. Final State:

Final Kinetic Energy (KE_f) = KE_i + Work Done

1. Calculate Initial Kinetic Energy:

Substitute the values for mass and initial velocity into the kinetic energy equation. Calculate the initial kinetic energy of the bicyclist: \[ KE_i = \frac{1}{2} \times 60 \times (2)^2 \]

1. Apply Conservation of Energy:

Use the conservation of energy principle to find the final kinetic energy: \[ KE_f = KE_i + 1,800 \] \[ KE_f = 60 + 1,800 = ? \]

1. Determine Final Velocity:

Once the final kinetic energy is known, use it to calculate the final velocity of the bicyclist: \[ \frac{1}{2} \times 60 \times v_f^2 = KE_f \]

1. Solution:

After solving the equation for final velocity, the numerical value obtained will represent the final velocity of the bicyclist after the increase in work output.

In conclusion, by applying the principles of work, energy, and velocity, the final velocity of the 60 kg bicyclist who initially traveled at 2 m/s and increased his work output by 1,800 J can be accurately determined. The integration of these fundamental concepts in physics leads to a comprehensive understanding of the bicyclist’s motion dynamics.