Posted by allan on Thursday, December 9, 2010 at 12:29am.
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
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