Final answer:
The athlete must exert 4000 joules of work to accelerate from standing still to their top running speed of 10 m/s, calculated using the work-energy principle and the athlete's mass of 80 kg.
Step-by-step explanation:
To calculate how many joules of work the athlete must exert to reach their top running speed, we can use the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) of an object with mass m moving at velocity v is given by the equation KE = (½)mv². In the case of the athlete who starts from rest (initial velocity, vi, is 0) and reaches a top speed of vf = 10 m/s, the work done to reach that speed can be found by calculating the change in kinetic energy, which is equal to the final kinetic energy since the initial kinetic energy is zero.
Using the athlete's mass, m = 80 kg, and top speed, v = 10 m/s, the kinetic energy at top speed would be KE = (½) × 80 kg × (10 m/s)² = 4000 joules. Therefore, the athlete must exert 4000 joules of work to accelerate from standing still to a top speed of 10m/s, ignoring frictional forces.