kinematics
posted by zachary .
these are two similar kinematics maths question which i don't know. Please help!
1)A particle moves in a straight line so that its distance, s metres, from a fixed point O is given by s = 2t^3  3t^2  12t + 6, where t is the time in seconds after passing O. Find the minimum speed attained by the particle
2)A particle moves in a straight line so that its distance, s meters, from a fixed point is given by s=t^3(2t)^2, where t is the time in seconds after passing through the fixed point. What is the greatest distance travelled by the particle?

kinematics 
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kinematics 
drwls
1) The speed at time t is
ds/dt = 6t^2 6t 12
(Speed is always positive)
The minimum value of ds/dt is 0 if there is a time when
6t^2 6t 12 = 0
t^2 t 2 = 0
(t2)(t+1) = 0
So there IS a time when the speed is zero.
2) The greatest value of s occurs at a time where ds/dt = 0 is the second derivative d^2/dt^2 at that time is negative.
s grows without bound for very large t greater than 2. I do not see how there could be a greatest value of s unless you restrict the region of consideration to 0 < t <2
t = 2 
kinematics 
drwls
In my answer to 2), "is" should be "if".
Sorry about that
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