A swimming pool is to be drained for cleaning. If L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and . How fast is the water running out at the end of 5 seconds? What is the average rate at which the water flows out during the first 5 seconds?
Given: L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and
To find: the rate of water running out of the pool at the last 5s. and also the average rate of water flowing at during the first 5s.
Explanation: Take the rate of Water running out given by
Given
Differentiation of the above-given equation results in,
Now, to find the speed of water running out at the end of 5s, we need to find the value of equation (i) with t=5
Therefore, 2000 L/s is the rate of water running out at the end of 5s
To calculate the initial rate we need to take t=o in equation (i)
Equation (ii) tells about the final rate of water flowing whereas equation (iii) is the initial rate.
Thus, the average rate during 5s is
After calculation, the final rate of water flowing out of the pool in 5s is 3000L/s.