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a particle moves along a straight line OX. at a time t(in seconds) the distance X(in metres) from the particle O is given by x=40+12t-t3. how long would the particle travel before coming to rest ...?

Answer :

You should consider when the velocity is zero

first i would take the derivative of the equation motion, leaving you with :
x = 12 - 3t^2

next, set the velocity to zero and solve t, which will give you 
√4 = t = +/- 2

Hope this helps

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