The required differential equation will be [tex]\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex] or [tex]\dfrac{d^2P(t)}{dt^2}-k\sqrt t=0[/tex].
Given information:
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.
Let a be the acceleration of the jogger.
So, the expression for acceleration can be written as,
[tex]a=\dfrac{d}{dt}(\dfrac{dP(t)}{dt})\\a=\dfrac{d^2P(t)}{dt^2}[/tex]
Now, the acceleration is proportional to square root of time.
So,
[tex]a\propto \sqrt t\\a=k\sqrt t\\\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex]
Therefore, the required differential equation will be [tex]\dfrac{d^2P(t)}{dt^2}=k\sqrt t[/tex] or [tex]\dfrac{d^2P(t)}{dt^2}-k\sqrt t=0[/tex].
For more details about differential equations, refer to the link:
https://brainly.com/question/1164377
