Final answer:
The average power needed to accelerate the 62-kg runner to a speed of 7.2 m/s in 2.3 s is approximately 699.76 watts. To sustain a constant speed of 7.2 m/s under a constant air resistance of 28 N, the average power needed is 201.6 watts.
Step-by-step explanation:
To solve this physics problem, we will calculate the average power needed to accelerate the runner and the average power needed to overcome air resistance at constant speed.
a) Average Power to Accelerate
The average power P needed by the runner to accelerate can be found using the formula:
P = Work / Time
= (Change in Kinetic Energy) / Time
The change in kinetic energy KE is given by ½ m v2, where m is the mass of the runner and v is the final velocity. Substituting our values:
KE = ½ × 62 kg × (7.2 m/s)2
= 1,609.44 J
The average power to accelerate the runner over a period of 2.3 seconds is then:
P = 1,609.44 J / 2.3 s
= 699.76 W
b) Average Power to Sustain Constant Speed
To calculate the average power to sustain a constant speed, we'll use the formula:
P = Force × Velocity
The runner experiences a constant air resistance of 28 N, and maintains a constant speed of 7.2 m/s.
Thus, the power needed is:
P = 28 N × 7.2 m/s
= 201.6 W