The cheetah is one of the fastest-accelerating animals, because it can go from rest to 18.2 m/s (about 41 mi/h) in 2.7 s. If its mass is 114 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in the following units
a) watts (w)
b) horsepower (hp)
a) Well, it seems the cheetah is quite the speed demon! To calculate its average power during acceleration, we'll need to use the formula for power: Power = Work/Time. Now, work is defined as force times distance, and in this case, the force will be the cheetah's mass times its acceleration. Since the cheetah starts from rest, we will use the final velocity of 18.2 m/s as the average velocity during the acceleration phase. So, the work done by the cheetah is (114 kg)(18.2 m/s), which gives us the amount of force applied. Next, we'll divide this work by the time it takes to accelerate (2.7 s). Doing the math, we get:
Power = (114 kg)(18.2 m/s) / (2.7 s)
b) Now, if you prefer horsepower instead of watts, we'll need to convert the answer. One horsepower is equal to 746 watts. So, to find the power in horsepower, we'll divide the power in watts by 746.
To determine the average power developed by the cheetah during the acceleration phase of its motion, we can use the formula for power:
Power = Force × Velocity
However, since we don't have the force directly given, we can calculate it using Newton's second law of motion:
Force = Mass × Acceleration
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 18.2 m/s
Time (t) = 2.7 s
Mass (m) = 114 kg
First, we need to calculate the acceleration:
Acceleration (a) = (v - u) / t
Acceleration (a) = (18.2 m/s - 0 m/s) / 2.7 s
Acceleration (a) = 18.2 m/s / 2.7 s
Acceleration (a) ≈ 6.74 m/s²
Now, we can calculate the force:
Force (F) = Mass (m) × Acceleration (a)
Force (F) = 114 kg × 6.74 m/s²
Force (F) ≈ 770.36 N
Finally, we can calculate the average power:
Average Power = Force (F) × Velocity (v)
Average Power = 770.36 N × 18.2 m/s
Average Power ≈ 14,017.35 watt (w)
To convert this to horsepower (hp), we can use the conversion factor:
1 hp = 746 w
Average Power (in hp) ≈ 14,017.35 w / 746 w/hp
Average Power ≈ 18.8 hp
So, the average power developed by the cheetah during the acceleration phase of its motion is approximately:
a) 14,017.35 watts (w)
b) 18.8 horsepower (hp)
To determine the average power developed by the cheetah during the acceleration phase of its motion, we can use the formula for power:
Power = Force x Velocity
First, we need to calculate the force applied by the cheetah during acceleration using Newton's second law of motion:
Force = mass x acceleration
The acceleration can be found using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Substituting the given values:
Initial Velocity (v₀) = 0 m/s
Final Velocity (v) = 18.2 m/s
Time (t) = 2.7 s
Acceleration = (18.2 m/s - 0 m/s) / 2.7 s
Acceleration = 6.74 m/s²
Now, we can calculate the force by multiplying the mass and the acceleration:
Force = 114 kg x 6.74 m/s²
Force = 768.36 N
Next, we can calculate the average power by multiplying the force and the velocity:
Power = Force x Velocity
Power = 768.36 N x 18.2 m/s
Power = 13,987.152 W
a) The average power developed by the cheetah during the acceleration phase of its motion is approximately 13,987.152 watts (W).
To convert the power to horsepower (hp), we can use the conversion factor:
1 horsepower (hp) = 745.7 watts (W)
b) Power (in horsepower) = Power (in watts) / 745.7
Power (in horsepower) = 13,987.152 W / 745.7
Power (in horsepower) = 18.76 hp
b) The average power developed by the cheetah during the acceleration phase of its motion is approximately 18.76 horsepower (hp).
Power is the rate of energy (here, kinetic energy) =>
P=W/t= mv²/2t = 114•18.2²/2•2.7 = 6993 W = =9.37 hp
1 hp = 745.66272 W