Kinematics - Maximum and Minimum Motion Quantities

A polar bear moves in a straight line to a food source and its path can be modelled by the equation \(s = 10t - t^2\) where \(s\) m is the distance from the nest at time \(t\) s.

The polar bear collects the food and then returns to its original location.

1. Find an expression for the velocity of the bear.
2. Find how far away the source of food is.
3. Find the length of time of the bear's journey.
4. What is the main problem with this model?

Use the model from departure at \(t=0\) until the first return to the nest. It is not a nonnegative distance-from-nest model beyond that journey.