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A particle moves along the x-axis, its position at time t is given by
x(t)= 5t/(10+7t^2)
where t is >= 0 and measured in seconds and x is in meters
The acceleration of the particle equals 0 at time t = ?
I took the 1st derivative and got
i got v(t ) = 5(10-7t^2) / (10+7t^2)^2
or i got v(t ) = 5(10-7t^2) * (10+7t^2)^-2
then i took the derivative of that and got:
a(t ) = 5[(10-7t^2)(-2)(10+7t^2)^(-3) *(14t) + (10+7t^2)^2 *(10-7t^2)]
so i tried factoring out (10-7t^2), to get one answer which i got as sqrt(10/7)
and then for the other answer i got:
(10+7t^2)^5 = 28t
which i simplified to:
2401t^8 + 13720t^6 + 29400t^4 + 28000t^2 - 28t + 10000 = 0
now I'm not sure if I'm on the right track, and if I am, I'm not sure how I can solve for t.
Any help is much appreciated, I've been working on this (my first problem) for about an hour and I have a midterm in a few days :s
thanks
x(t)= 5t/(10+7t^2)
where t is >= 0 and measured in seconds and x is in meters
The acceleration of the particle equals 0 at time t = ?
I took the 1st derivative and got
i got v(t ) = 5(10-7t^2) / (10+7t^2)^2
or i got v(t ) = 5(10-7t^2) * (10+7t^2)^-2
then i took the derivative of that and got:
a(t ) = 5[(10-7t^2)(-2)(10+7t^2)^(-3) *(14t) + (10+7t^2)^2 *(10-7t^2)]
so i tried factoring out (10-7t^2), to get one answer which i got as sqrt(10/7)
and then for the other answer i got:
(10+7t^2)^5 = 28t
which i simplified to:
2401t^8 + 13720t^6 + 29400t^4 + 28000t^2 - 28t + 10000 = 0
now I'm not sure if I'm on the right track, and if I am, I'm not sure how I can solve for t.
Any help is much appreciated, I've been working on this (my first problem) for about an hour and I have a midterm in a few days :s
thanks