Final answer:
It takes 30 seconds for a 2.5 kW electric motor to do 75,000 J of work, calculated by dividing the total work by the power output of the motor.
Step-by-step explanation:
To determine how long it takes a 2.5 kW (2,500 watts) electric motor to do 75,000 J of work, we use the relationship between power, work, and time. Power is the rate at which work is done and is expressed as work divided by time (P = W/t), which can be rearranged to find time (t = W/P).
Given that 1 watt equals 1 joule per second, a 2.5 kW motor produces 2,500 joules per second. To find the time it takes for the motor to perform 75,000 J of work, divide the total work by the power output:
t = 75,000 J / 2,500 J/s
t = 30 seconds
Therefore, it takes 30 seconds for the 2.5 kW electric motor to do 75,000 J of work.