The displacement of a particle is given by s=2t^3 - 9t^2 + 12t - 5, where s is the displacement in metres at time, t seconds. a) When is the speed of the particle 36m per second? b) What is the acceleration of the particle at this time?
a. I willl assume you know the power rule so s'=6t²-18t+12 solve when s'=36 36=6t²-18t+12 6=t²-3t+2 0=t²-3t-4 0=(t-4)(t+1) set to zero t-4=0 t=4 t+1=0 t=-1, false no negative times allowed
at t=4 or 4 seconds
b. at t=4 take deritive again s''=12t-18 at t=4 s''=12(4)-18 s''=48-18 s''=30 acceleartion is 30mpsps
