If an 80-kg sprinter can accelerate from a standing start to a speed of 10 m/s in 3 s, what average power is generated?
(Kinetic energy change)/(Time)
= (1/2)MV^2/T
The answer will be in watts if M is in kg, V is in m/s and T is in seconds
To calculate the average power generated by the sprinter, we can use the equation:
Power = (Force x Distance) / Time
To find the force exerted by the sprinter, we can use Newton's second law of motion:
Force = mass x acceleration
Given:
Mass (m) = 80 kg
Acceleration (a) = Change in velocity / Time taken = (Final velocity - Initial velocity) / Time = (10 m/s - 0 m/s) / 3 s
Calculating acceleration:
a = (10 m/s - 0 m/s) / 3 s
a = 10 m/s / 3 s
a ≈ 3.333 m/s^2
Calculating force:
Force = mass x acceleration
Force = 80 kg x 3.333 m/s^2
Calculating the power:
Power = (Force x Distance) / Time
Since the distance is not given, we can assume the sprinter runs for 100 meters or any other convenient distance.
Power = (Force x Distance) / Time
Power = (80 kg x 3.333 m/s^2 x 100 m) / 3 s
Calculating the average power:
Power = (8000 kg m^2/s^2) / 3 s
Power = 2666.67 W
Therefore, the average power generated by the sprinter is approximately 2666.67 Watts (W).
To find the average power generated by the sprinter, we can use the equation:
Power = Work / Time
In this scenario, the work done by the sprinter is equal to the change in kinetic energy, which can be calculated as:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Given:
Mass (m) = 80 kg
Initial Velocity (v1) = 0 m/s (since the sprinter starts from a standing position)
Final Velocity (v2) = 10 m/s
Time (t) = 3 s
First, let's calculate the work done:
Work = (1/2) * 80 kg * (10 m/s)^2
= (1/2) * 80 kg * 100 m^2/s^2
= 4000 Joules
Next, we can substitute the values into the formula for power:
Power = Work / Time
= 4000 J / 3 s
≈ 1333.33 Watts
Therefore, the average power generated by the sprinter is approximately 1333.33 Watts.