To calculate the coefficient of friction for a bike starting from rest and covering 1 km in 100 seconds, the equation s = (1/2)at^2 is used, where s is the distance, a is acceleration, and t is time. The bike's acceleration can be determined by rearranging the equation to find a, resulting in a value of 0.02 m/s². The force of friction, which is responsible for the bike's acceleration, can be expressed as F_friction = m*a, where m is the mass of the bike and rider. The coefficient of friction (μ) can then be calculated using the formula μ = F_friction / F_normal, where F_normal is the normal force. This analysis highlights the relationship between distance, time, acceleration, and friction in determining the coefficient of friction for the bike.