If a 65 kg sprinter can accelerate from a standing start to a speed of 12 m/s in 3 s, what average power is generated?
P = 0.5M*V^2/t = 0.5*65*12^2/3 = 1560 J/s = 1560 Watts
Well, if the sprinter is generating power, they must be running on some kind of high-performance battery. Is it made by Energizer or Duracell? Just kidding! Let's calculate the average power generated by our sprinter friend, shall we?
To find the average power, we need to know the work done in that time period. Work is equal to force multiplied by distance, and in this case, it's also given by the formula work equals change in kinetic energy.
The change in kinetic energy is given by 1/2 multiplied by the mass of the sprinter multiplied by the final velocity squared. So, (1/2) * 65 kg * (12 m/s)^2. Don't worry, I'll do the math for you.
(1/2) * 65 kg * (12 m/s)^2 = 46,800 Joules
Since power is equal to work divided by time, we can now calculate the average power generated. 46,800 Joules / 3 seconds = 15,600 Watts (or joules per second).
So, our sprinter generates an average power of 15,600 Watts. That's quite a lot of power! Just be careful not to blow any fuses with all that energy.
To find the average power generated by the sprinter, we can use the formula:
Power = Work / Time
First, let's find the work done by the sprinter. The work done can be calculated using the formula:
Work = Force x Distance
Since the sprinter is starting from a standing position and accelerating to a speed, the force applied can be calculated using Newton's second law:
Force = Mass x Acceleration
Given:
Mass (m) = 65 kg
Acceleration (a) = Change in velocity / Time = (12 m/s - 0 m/s) / 3 s = 4 m/s^2 (since the sprinter starts from rest)
Using this, the force applied can be calculated as:
Force = Mass x Acceleration
= 65 kg x 4 m/s^2
= 260 N
Next, let's calculate the distance traveled. The average speed can be calculated using the formula:
Average Speed = Total Distance / Total Time
The sprinter starts from rest and reaches a speed of 12 m/s in 3 seconds. Therefore, the average speed can be calculated as:
Average Speed = (12 m/s + 0 m/s) / 2 = 6 m/s
The total distance traveled can be calculated using the formula:
Distance = Average Speed x Time
Distance = 6 m/s x 3 s
= 18 m
Now, we can find the work done:
Work = Force x Distance
= 260 N x 18 m
= 4680 J (joules)
Finally, we can find the average power generated by the sprinter:
Average Power = Work / Time
= 4680 J / 3 s
= 1560 Watts or 1.56 kW
Therefore, the average power generated by the sprinter is 1.56 kW.
To find the average power generated by the sprinter, we need to use the formula:
Power = Work / Time
In this case, the work done by the sprinter can be calculated using the formula:
Work = Force x Distance
First, we need to find the force exerted by the sprinter. We can use Newton's second law of motion to calculate the force:
Force = Mass x Acceleration
Given that the mass of the sprinter is 65 kg, and the sprinter accelerates from a standing start to a speed of 12 m/s in 3 s, we can calculate the acceleration as follows:
Acceleration = (Final Velocity - Initial Velocity) / Time
= (12 m/s - 0 m/s) / 3 s
= 4 m/s²
Now we can calculate the force:
Force = Mass x Acceleration
= 65 kg x 4 m/s²
= 260 N
Next, we need to find the distance traveled by the sprinter during the acceleration phase. Since the sprinter starts from a standing start, we can assume that the initial velocity is 0 m/s. We can calculate the distance using the formula:
Distance = (Final Velocity^2 - Initial Velocity^2) / (2 x Acceleration)
= (12 m/s)^2 - (0 m/s)^2 / (2 x 4 m/s²)
= 144 m²/s² / 8 m/s²
= 144 / 8 m
= 18 m
Now we can calculate the work done by the sprinter:
Work = Force x Distance
= 260 N x 18 m
= 4680 N·m or J (Joules)
Finally, we can calculate the average power using the work and time values:
Average Power = Work / Time
= 4680 N·m / 3 s
= 1560 W (Watts)
Therefore, the average power generated by the sprinter is 1560 Watts.