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

a particle moves along the x-axis 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**, Thursday, December 9, 2010 at 8:49am
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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