A train driver is driving along and he suddenly puts on the brakes. After he holds the brakes for t seconds, the train's sliding distance can be measured as d(t)=30t−0.6t^2 (in meters). When the train stops, how far did the train slide (in meters) after the train driver put on the brakes?
when the train stops d ' (t) = 0 , or the velocity is zero
v(t) = d ' (t) = 30 - 1.2t
= 0
1.2t = 30
t = 25
it will slide for 25 seconds and the distance is
d(50) = 30(25) - .6(25)^2 = 375 metres.