Question

The speed s of an object dropped from rest varies with the distance y it has fallen according to the equation s=2gy−−−√ , where g is the acceleration due to gravity. What is the instantaneous rate of change of the speed with respect to distance? (1 point)

Answer 1

To find the instantaneous rate of change of the speed with respect to distance, we need to find the derivative of the speed equation with respect to distance.

Using the power rule and chain rule, we can find:

ds/dy = d/dy (2gy^0.5)
= 2g * 0.5 * y^(-0.5)
= g * y^(-0.5)

Therefore, the instantaneous rate of change of the speed with respect to distance is g * y^(-0.5).