A 60.0 kg person accelerates from rest to 12 m/s in 6.0 seconds. What is the person’s power?
To find the person's power, we can use the formula:
Power = Force × Velocity
First, let's find the force. The force required to accelerate an object is given by Newton's second law:
Force = mass × acceleration
The acceleration can be calculated using the formula:
acceleration = change in velocity / time
Given that the initial velocity (u) is 0 m/s, the final velocity (v) is 12 m/s, and the time (t) is 6.0 seconds, we can substitute these values into the formula to find the acceleration:
acceleration = (v - u) / t
acceleration = (12 - 0) / 6.0
acceleration = 2.0 m/s^2
Now, substitute the mass (m) and acceleration (a) into the formula for force:
Force = mass × acceleration
Force = 60.0 kg × 2.0 m/s^2
Force = 120 N
Finally, substitute the force (F) and velocity (v) into the formula for power:
Power = Force × Velocity
Power = 120 N × 12 m/s
Power = 1440 W
Therefore, the person's power is 1440 Watts.