We can use the formula:
Power = Work / Time
Power is given as 100 watts, the work done is equal to the force required to lift the crate multiplied by the distance lifted. The force required is equal to the weight of the crate, which is:
Force = mass x acceleration due to gravity
Force = 20 kg x 9.81 m/s^2 = 196.2 N
So, the work done is:
Work = Force x Distance
Work = 196.2 N x 2.5 m = 490.5 J
Now, we can solve for time:
Time = Work / Power
Time = 490.5 J / 100 watts = 4.905 seconds
Therefore, the fastest time that could be used to lift the crate without exceeding 100 watts of power is approximately 4.9 seconds.
It'd be 5 Seconds!