6. A particle moving along a straight line has a velocity given by v = 4 − x², where v is the velocity in ft/sec and x is the position in ft. = 1 ft. (a = −6 ft/sec²) (a) Determine the acceleration of the particle at position x = (b) Determine the travel time from the origin to the position x = 1 ft. (t = 0.275 sec) (c) Show that the particle never arrives at position x = 2 ft. (t = ∞) 1 1 Hint: ±² = 1½ (2²±² + 2 + 2). 4 x 2-x

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Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…