the cheetah is is one of the fastest accelerating animals, for it can go from rest to 34.5 m/s in 5.00 seconds. if its mass is 106 kg, determine the average powee developes by the cheetah during the acceleration phase of its motion
P=F*V = mg*V = 106*9.8 * 34.5=35,839 J/s
=35,839 Watts.
To determine the average power developed by the cheetah during the acceleration phase of its motion, we can use the formula for power:
Power = Work / Time
The work done by the cheetah during acceleration can be calculated using the formula:
Work = Force * Distance
The force required to accelerate an object can be found using Newton's second law:
Force = mass * acceleration
First, let's find the force using the given values:
Mass of the cheetah, m = 106 kg
Acceleration, a = change in velocity / time = (final velocity - initial velocity) / time = (34.5 m/s - 0 m/s) / 5.00 s
Now, we can calculate the force:
Force = mass * acceleration
Force = 106 kg * ((34.5 m/s - 0 m/s) / 5.00 s)
Next, we need to determine the distance traveled by the cheetah during acceleration. This can be found using the kinematic equation:
Distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the cheetah starts from rest, the initial velocity is 0 m/s:
Distance = 0.5 * acceleration * time^2
Distance = 0.5 * ((34.5 m/s - 0 m/s) / 5.00 s) * (5.00 s)^2
Now that we have both the force and distance, we can calculate the work done by the cheetah:
Work = Force * Distance
Finally, we can determine the average power developed by the cheetah during the acceleration phase of its motion:
Power = Work / Time
Plug in the calculated values to get the answer.