Question

Given the position function, SEE BELOW, between t = 0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right.

3 < t < 9
5 < t < 9
The particle never moves to the right.
The particle always moves to the right.

Answer 1

Position function
s(t)=-t^3/3+13t^2/2-30t
velocity function
v(t)=s'(t)=-t^2+13t-30
For particle to move to the right (positive x-axis), v(t)>0.
Solve v(t)=0
v(t)=0 when t=3 or t=10
Since leading term of v(t) is negative, the maximum is between t=3 and t=10, i.e.
v(t)>0 for 3<t<10.
Since the domain of t is [0,9], so the particle moves to the right for 3<t<9,
i.e. reject the interval (9,10).