A particle moves along the x-axis so that at any time t>=0 its velocity is v(t)=9-t^2. If at t=1,is x=2, what is the position of the particle when it is furthest right on the x-axis .

Answer 1

x(t) = 9t - 1/3 t^3 + c
since x(1)=2,
2 = 9 - 1/3 + c
c = -20/3

x(t) = 9t - 1/3 t^3 - 20/3

when v=0, the particle has changed direction. That is when t=3.

So, now just evaluate x(3).