Question
35. A 62-kg runner starts from rest and reaches a speed of 7.2m/s in 2.3 s with negligible air resistance.The runner then runs the remainder of the race at a constant speed of 7.2m/s under the influence of a constant alr resistance of 28 N. a) Find the average power needed to accelerate the runner. b) Find the average power needed to sustain the constant speed of 7.2m/s for the remainder of the race.
Solution
4.7
(247 Votes)
Ulysses
Veteran · Tutor for 9 years
Answer
**a) Average Power to Accelerate:*** **Work done (W):** The work done to accelerate the runner is equal to the change in kinetic energy. W = ΔKE = (1/2)mv² - (1/2)mu² Since the runner starts from rest, initial velocity (u) = 0. W = (1/2) * 62 kg * (7.2 m/s)² = 1607.04 J* **Time (t):** The time taken for acceleration is given as 2.3 s.* **Average Power (P):** Power is the rate of doing work. P = W/t = 1607.04 J / 2.3 s = **698.71 W** (approximately)**b) Average Power to Sustain Constant Speed:*** **Force (F):** To maintain a constant speed, the runner must exert a force equal to the air resistance. F = 28 N* **Velocity (v):** The constant speed is given as 7.2 m/s.* **Power (P):** The power required to sustain this speed is given by: P = F * v = 28 N * 7.2 m/s = **201.6 W**Therefore, the average power needed to accelerate the runner is approximately 698.71 W, and the average power needed to sustain the constant speed is 201.6 W.