Answer:
a)x = 100.56
b) t = 2.25 s
Step-by-step explanation:
given equation
x = 4 t³ - 27 t² + 17 t + 8
to get velocity we need to differentiate the expression w.r.t time

on solving the differential equation
v = 12 t² -54 t + 17
at v = 0
using quadratic equation to solve
we get

t = 4.16 s and 0.34 s
x = 4 × 4.16³ - 27 × 4.16² + 17 × 4.16 + 8
x = -100.56
x = 100.56
b) v = 12 t² -54 t + 17
to get acceleration we need to differentiate the expression w.r.t time

on solving the differential equation
a = 24 t -54
time at which acceleration will be zero
24 t = 54
t = 2.25 s