Final answer:
The average power developed by the cheetah during the acceleration phase is approximately 10485.57 watts or 14.06 horsepower. This is calculated using the cheetah's acceleration, force, and velocity, with the final conversion to horsepower using the standard conversion rate.
Step-by-step explanation:
To determine the average power developed by the cheetah during the acceleration phase, we can use the formula P = (F × v) / 2, where P is the power, F is force, and v is velocity. The force can be found using Newton's second law F = m × a, where m is mass and a is acceleration.
First, let's find the cheetah's acceleration (a) by using the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time.
- Δv = final velocity - initial velocity = 31.5 m/s - 0 m/s = 31.5 m/s
- Δt = 4.78 s
- a = 31.5 m/s / 4.78 s = 6.59 m/s²
Now, we can calculate the force:
- F = m × a = 101 kg × 6.59 m/s²
- F = 665.59 N
Next, calculate the average power in watts:
- P = (F × v) / 2 = (665.59 N × 31.5 m/s) / 2
- P = 10485.57 W
To convert this to horsepower (hp), use the conversion 1 hp = 745.7 W:
- P = 10485.57 W / 745.7 W/hp
- P ≈ 14.06 hp
The average power developed by the cheetah during the acceleration phase of its motion is approximately 10485.57 watts or 14.06 horsepower.