A woman runs a kilometer using a force of 210 N and a power output of 500 W. How long in minutes does it take this woman to complete 1 kilometer?
Power= force*distance/time
solve for time in seconds, then convert to minutes.
To find the time it takes for the woman to complete 1 kilometer, we can use the formula:
Power = Work / Time
In this case, the power output is given as 500 W. Since power is defined as work done per unit time, we can rewrite the formula as:
Power = (Force * Distance) / Time
Rearranging the formula, we get:
Time = (Force * Distance) / Power
Substituting the given values:
Time = (210 N * 1 km) / 500 W
We need to convert the distance from kilometers to meters since the force is given in newtons and the power in watts. There are 1000 meters in 1 kilometer, so:
Time = (210 N * 1000 m) / 500 W
Simplifying the expression:
Time = (210,000 m * N) / 500 W
Since N and W are equivalent units, we can cancel them out:
Time = (210,000 m) / 500
Evaluating the expression, we find:
Time = 420 minutes
Therefore, it takes this woman approximately 420 minutes to complete 1 kilometer.
To determine the time it takes for the woman to complete 1 kilometer, we need to use the formula:
Power = Force * Velocity
Rearranging the formula to solve for velocity:
Velocity = Power / Force
Given that the force is 210 N and the power output is 500 W, we can substitute the values into the formula:
Velocity = 500 W / 210 N
Now, we need to convert the velocity from meters per second (m/s) to kilometers per minute (km/min). Since 1 kilometer is equal to 1000 meters and 1 minute is equal to 60 seconds, we can use the conversion factor:
Velocity (km/min) = Velocity (m/s) * (1000 m / 1 km) * (1 min / 60 s)
Now we can substitute the velocity value into the formula:
Velocity (km/min) = (500 W / 210 N) * (1000 m / 1 km) * (1 min / 60 s)
Simplifying the expression:
Velocity (km/min) = (500 * 1000) / (210 * 60) km/min
Velocity (km/min) ≈ 3.968 km/min (rounded to 3 decimal places)
Therefore, it takes the woman approximately 3.968 minutes (or about 3 minutes and 58 seconds) to complete 1 kilometer.