A graphing calculator is recommended.A particle moves according to a law of motion s = f(t), t≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)f(t) = t³ 9t² + 24t(a) Find the velocity (in ft/s) at time t.v(t) =(b) What is the velocity (in ft/s) after 1 second?v(1) =t =(c) When is the particle at rest? (Enter your answers as a comma-separated list.)(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)(e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.fta(t) =(f) Find the acceleration (in ft/s2) at time t.ft/s²ft/sFind the acceleration (in ft/s²) after 1 second.a(1) =ft/s²30ft/s(g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6.2010- 10a1456t302010ggt561-10When is it slowing down? (Enter your answer using interval notation.)302010- 10(h) When is the particle speeding up? (Enter your answer using interval notation.)a124a2456302010-10Va12456t

Topic = Algebra As per guidelines , At a time only three sub-parts of a question can be answered.…

A particle moves according to a law of motion s= f(t), tz 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t)=³-9² +24t (a) Find the velocity (in ft/s) at time t. v(t) = ft/s (b) What is the velocity (in ft/s) after 1 second? v(1) = ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.)