Calculating the Work Done to Increase the Speed of a Bicycle

To calculate the work done on a bicycle to increase its speed, we can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.

Given:
Mass of the bicycle (m) = 20 kg
Initial speed (v_i) = 2 m/s
Final speed (v_f) = 5 m/s

Step 1: Calculating the Initial Kinetic Energy (KE_i)
The initial kinetic energy of the bicycle can be calculated using the formula:
KE_i = (1/2) * m * v_i^2

Substituting the given values:
KE_i = (1/2) * 20 kg * (2 m/s)^2
KE_i = 40 J

Step 2: Calculating the Final Kinetic Energy (KE_f)
The final kinetic energy of the bicycle can be calculated using the formula:
KE_f = (1/2) * m * v_f^2

Substituting the given values:
KE_f = (1/2) * 20 kg * (5 m/s)^2
KE_f = 250 J

Step 3: Calculating the Work Done (W)
The work done on the bicycle to increase its speed can be calculated by finding the difference between the final and initial kinetic energies:
W = KE_f - KE_i

Substituting the calculated values:
W = 250 J - 40 J
W = 210 J

Therefore, the work done on the bicycle to increase its speed from 2 m/s to 5 m/s is 210 Joules.

Explanation:
Work is done on an object when a force is applied to it, causing it to move. In this case, the work is done by the cyclist who applies a force to the pedals, transferring energy to the bicycle. The work done increases the kinetic energy of the bicycle, resulting in an increase in speed.

The calculation involves determining the initial and final kinetic energies of the bicycle. The initial kinetic energy is calculated using the mass and initial speed of the bicycle. The final kinetic energy is calculated using the mass and final speed of the bicycle.

The work done is then obtained by subtracting the initial kinetic energy from the final kinetic energy. This represents the additional energy transferred to the bicycle to increase its speed. In this scenario, the work done is found to be 210 Joules.