A particle moves along the x-axis so that at time t\ge 0t≥0 its velocity is given by v(t)=3t^2+6t-9.v(t)=3t 2 +6t−9. Determine all values of tt when the particle is at rest.

Question

A particle moves along the x-axis so that at time t≥0 its velocity is given by v(t)=3t^2+6t−9. Determine all values of t when the particle is at rest.

Answer 1

When the particle is at rest, it means v(t)=0. 

0=3t²+6t−9

0 = 3(t²+2t−3)

0 = 3(t + 3)(t-1)

t+3 = 0, t-1=0

t = -3,1

-3 is extraneous because you can't have a negative time (t≥0)

t=1