(7) Consider a particle moving along a straight line whose position function is s(x) = 4t - t2, where s is in feet and t is in seconds. Find the average velocity of of the particle from t = 1 second to t = 3 second and the instantaneous velocity at t = 1 sec. (A) The average V1,3] A=0ft/s; the instantaneous velocity v(1)=z=1=2ft/s (B) The average V1,3] == 0ft/s; no instantaneous velocity for no change at t = 1s. (C) The average velocity V₁1,3] == 2 ft/s and v(1) = -1 = 0ft/s -1 = 2 ft/s (D) The average velocity V₁1,3] = A= v(1) = =

Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches

8) A runner was training for a 21 mile long race. The distance D (in miles) in function of time t (in weeks) is given by: D = 2(t-1)² +15 a) b) c) How many miles have done the runner in the first week? What is the average rate of training between the first and the third week? dD Calculate the derivative of D with respect to time dt and explain the obtained answer.

Consider the curve x3 + y2 - 4xy = -2