a power = work/time question.
A broken car is being pushed to a garage.
a) work out the drivers output if he takes 1 hour and 45 mins to push his car 2km with a force of 900N.
b) work out the total power output if the driver has to stop for a 30 minute kip halfway.
c) the driver's maximum power output is 500W. how long would it take him to push the car to the garage at maximum output?
To solve these questions, we need to understand the formula for power, which is:
Power = Work / Time
a) To work out the driver's output, we first need to calculate the work done. The formula for work is:
Work = Force x Distance
Given that the distance is 2 km and the force is 900 N, we can calculate the work done as follows:
Work = 900 N x 2 km = 1800 N•km
Now, let's convert the time given to hours. Since 1 hour and 45 minutes is equivalent to 1.75 hours, we have:
Time = 1.75 hours
Using the formula for power, we can now calculate the driver's output:
Power = Work / Time
Power = 1800 N•km / 1.75 hours
b) In this case, the driver stops for a 30-minute break halfway. So the total time taken would be 1 hour and 45 minutes (1.75 hours) + 0.5 hours (the 30-minute break). Therefore:
Time = 1.75 hours + 0.5 hours = 2.25 hours
Using the formula for power, we can calculate the total power output:
Power = Work / Time
Power = 1800 N•km / 2.25 hours
c) The driver's maximum power output is given as 500 W. To determine how long it would take him to push the car to the garage at maximum output, we rearrange the power formula:
Power = Work / Time
Since we are given the power and work, we can substitute these values into the formula:
500 W = 1800 N•km / Time
Now, rearranging the formula to solve for Time:
Time = 1800 N•km / 500 W
This will give us the time in hours that the driver would take to push the car to the garage at maximum output.