a 5-kilowatt source powers a motor that is lifting a 30 kg mass straight up. how far will the mass move in 6 seconds

To calculate the distance the mass will move, we need to use the formula:

Work = Force x Distance

Since the mass is being lifted straight up, the force can be calculated using Newton's second law:

Force = Mass x Acceleration

Acceleration due to gravity is approximately 9.8 m/s². Therefore:

Force = 30 kg x 9.8 m/s²

Now, we can find the work done by the motor in 6 seconds using the formula:

Work = Power x Time

The power is given as 5 kilowatts, which needs to be converted to watts:

Power = 5 kilowatts x 1000 = 5000 watts

Finally, we can find the distance using the equation:

Work = Force x Distance

Substituting the values:

5000 watts x 6 seconds = Force x Distance

Now, rearrange the equation to solve for distance:

Distance = (5000 watts x 6 seconds) / (Force)

Plugging in the value for force:

Distance = (5000 watts x 6 seconds) / (30 kg x 9.8 m/s²)

Calculating:

Distance = 30,000 joules / (294 Newtons)

Distance ≈ 102 meters

Therefore, the mass will move approximately 102 meters in 6 seconds when powered by a 5-kilowatt source.