The required differential equation will be or .
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,
Now, the acceleration is proportional to square root of time.
So,
Therefore, the required differential equation will be or .
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