An object moves horizontally along a line. Its position from a fixed point can be modelled by s(t) = t^3 - 6t^2 - 15t + 20, where s is the displacement, in cm, and t is the time. in seconds. Determine the object's maximum velocity on the interval 0 ≤ t ≤ 5.

(I got an answer of 0 cm per second as the maximum velocity, just checking if anyone else has got the same thing) (Calculus - Optimisation)

Question

An object moves horizontally along a line. Its position from a fixed point can be modelled by s(t) = t^3 - 6t^2 - 15t + 20, where s is the displacement, in cm, and t is the time. in seconds. Determine the object's maximum velocity on the interval 0 ≤ t ≤ 5.

(I got an answer of 0 cm per second as the maximum velocity, just checking if anyone else has got the same thing) (Calculus - Optimisation)

anonymous · Answer

$$
v(t) = s'(t) \
a(t) = v'(t)=s''(t)
$$If acceleration $a(t)=0$, we have critical numbers of velocity.

What did you get for these functions?