The position

The position of a body at any time T is given by the displacement function S=t3-2t2-4t-8. Find its acceleration at each instant time when the velocity is zero.

Correct result:

a =  8

Solution:

s=t32t24t8 v=ds/dt=3t24t4 a=dv/dt=6t4 v=0  3t24t4=0  3 t24 t4=0 3t24t4=0  a=3;b=4;c=4 D=b24ac=4243(4)=64 D>0  t1,2=b±D2a=4±646 t1,2=4±86 t1,2=0.66666667±1.33333333333 t1=2 t2=0.666666666667   Factored form of the equation:  3(t2)(t+0.666666666667)=0  t>0 a=6 t14=6 24=8

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