An automobile starts from rest and travels down a straight section of road. The distance s (in feet) of the car from the starting position after t seconds is given by s(t) = 3t3. (a) Find the instantaneous velocity (in feet per second) at t = 2 seconds. Instantaneous velocity at t = 2 is At /s . (b) Find the instantaneous velocity in (feet per second) at t = 7 seconds. Instantaneous velocity att = 7 is ft / s .The equation of motion of a particle is s = t* - 4t, where s is in meters and t is in seconds. Assuming that t 2 0, answer the following questions. 1. Find the velocity v as a function of t. Answer: v(t) = 2. Find the acceleration a as a function of t. Answer: a(t) = 3. Find the acceleration after 2 seconds. Answer (in m/s): a(2) = 4. Find the acceleration when the velocity is 0. Answer (in m/s ): a =The population of a slowly growing bacterial colony after t hours is given by p(t) = 5t2 + 24t + 100. Find the growth rate after 4 hours. Answer:A Spherical balloon is being inated. Find a general formula for the instantaneous rate of change of the volume V with respect to the radius 1: given that V z E: . 3 Answer: C] Find the rate of change of V with respect to r at the instant when the radius is 1' = 5. Answer: [ I The force F on an object is the product of the mass m. and the acceleration a. In this problem, assume that the mass and acceleration both depend on time t, hence so the does the force. That is, Fl!) = 174000!) At time t : 8 seconds, the mass of an object is 72 grams and changing at a rate of 3%. At this same time, the acceleration is 8% and changing at a rate of 76%. By the product rule, the force on the object is changing at the rate of Please include units in your answer (click the link for help].. To enter compound units use multiplication, division, and exponent symbols, e.g., use ft 2k lb for footipounds or 111/32 tor meters per second per second. 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) = t* - 162t2 + 6561, If appropriate, enter answers in radical form. Use inf to represent co. (a) Find the velocity and acceleration functions. v(t): a(t): (b) Find the position, velocity, speed, and acceleration att = 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. t=1Suppose that a particle moves according to the law of motion s:t29t+29, tau. (A) Find the velocity at time t. 1.10:) :Cl (B) What is the velocity after 3 seconds? Velocity after 3 seconds : l' (C) Find all values of i tor which the particle is at rest. (If there are no such values, enter 0. If there are more than one valuer list them separated by commas.) an (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 = '1