The position of a test vehicle along a straight track is modelled by s=t3−9t2+24ts=t^3-9t^2+24ts=t3−9t2+24t metres for 0≤t≤80\leq t\leq80≤t≤8.
Find the maximum speed predicted by the model at the endpoints or at an instant when the acceleration is zero.
Give one reason why this polynomial model should not be extrapolated indefinitely.