Posted by allan on .
a particle moves along the xaxis in such a way that its acceleration at any time t is given by a(t)= 6t  18. At time t = 0, the velocity v(t) = 24. and at time t = 1, the position x(t) = 20
i have to find the expression for the velocity and what values t is at rest

calculus 
Reiny,
since a(t) = 6t 18
v(t) = 3t^2  18 + c
but we are told v(0) = 24
so 24 = 0 + 0 + c, > c = 24
if v(t) = 3t^2  18t + 24
x(t) = t^3  9t^2 + 24t + k
but we are told x(1) = 20
so 20 = 1  9 + 24 + k , > k = 4
x(t) = t^3  9t^2 + 24t + 4
Your last sentence is confusing.
Did you mean " ... and what values of t the particle is at rest" ?
anyway, since you now have all 3 equations, I am pretty sure you can proceed from there