Question

A jogger runs along a straight track. The jogger’s position is given by the function p(t), where t is measured in minutes since the start of the run. During the first minute of the run, the jogger’s acceleration is proportional to the square root of the time since the start of the run. Write a differential equation that describes this relationship, where k is a positive constant?

Answer 1

Answer:

$\frac{d^{2}p}{dt^{2}}=k*\sqrt{t}$

Step-by-step explanation:

Given

The jogger’s position: p(t)

We can express the acceleration a as follows

$a=\frac{d^{2}p}{dt^{2}}$

then

$\frac{d^{2}p}{dt^{2}}=k*\sqrt{t}$

only if

 $0 min\leq t\leq 1 min$