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The equation of motion of a particle is s=t55t, where s is in meters and t is in seconds. Assuming that t0, answer the following questions. 1. Find the velocity v as a function of t. Answer: v(t)= 5 Theequationo f motiono faparticleiss =t55t, wheresi sin metersandti sinsec onds.Assu n 2. Find the acceleration a as a function of t. Answer: a(t)= 3. Find the acceleration after 2 seconds. Answer (in m/s2):a(2)= 4. Find the acceleration when the velocity is 0 . Answer (in m/s2 ): a= The population of a slowly growing bacterial colony after t hours is given by p(t)=5t2+28t+100. Find the growth rate after 3 hours. Answer: A Spherical balloon is being inflated. Find a general formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V=34r3. Answer: Find the rate of change of V with respect to r at the instant when the radius is r=5. Answer: The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(t)=t4162t2+6561,t0 If appropriate, enter answers in radical form. Use inf to represent . (a) Find the velocity and acceleration functions. v(t):a(t): (b) Find the position, velocity, speed, and acceleration at t=2. Position (ft): Velocity (ft/sec) : Speed (ft/sec): Acceleration ( ft/sec2) : (c) At what times is the particle stopped? Enter as a comma-separated list. Suppose that a particle moves according to the law of motion s=t27t+20,t0 (A) Find the velocity at time t. v(t)= (B) What is the velocity after 3 seconds? Velocity after 3 seconds = (C) Find all values of t for which the particle is at rest. (If there are no such values, enter 0 . If there are more than one value, list them separated by commas.) t= (D) Use interval notation to indicate when the particle is moving in the positive direction. (If the particle is never moving in the positive direction, enter " { " without the quotation marks.) Answer =