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?

Speed=s'
acceleration=s''

take derititive to find speed

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

a. at t=4
b. 30 meters per second per second

It seems like a lot of movies