A fluid particle flowing along a stagnation streamline, as shown in Video V4.9 and Fig. P4.35, slows down as it approaches the stagnation point. Measurements of the dye flow in the video indicate that the location of a particle starting on the stagnation streamline a distance s = 0.8 ft upstream of the stagnation point at t = 0 is given approximately by s = 0.8e-0.61t where t is in seconds and s is in feet.(a) Factor the relation for the speed as a function of position out of the relation for speed as a function of time. What is the expression for speed V in terms of position s only?(b) For the position as a function of time given in the problem, what is the relation between the speed of the particle V and time t?(c) Symbolically, what does the derivative of position with respect to time equal?