Derivative application question? 10 points WILL be rewarded!?

A subway train travels from one station to the next in 2 mins. It's distance, in kilmeters, from the first station after t minutes is

s(t) = t^2 - 1/3 (t)^3 . At what times will the train have a velocity of 0.5 km/min.



Show your work, please :)Derivative application question? 10 points WILL be rewarded!?
s(t) = t虏 - 1/3 t鲁

v(t) = d/dt s(t)

v(t) = d/dt (t虏 - 1/3 t鲁) = 2t - t虏



1/2 km/min = 2t - t虏

t虏 - 2t = -1/2

t虏 - 2t + 1 = -1/2 + 1

(t - 1)虏 = 1/2

t - 1 = 卤鈭?1/2) = 卤鈭?/2

t = 卤鈭?/2 + 1



Answer: t = (鈭?/2 + 1) min, (-鈭?/2 + 1) min

Derivative application question? 10 points WILL be rewarded!?
v = ds/dt = 2t - t^2 = 0.5



or

t^2 -2t +0.5 =0



solve for t



t= (2 +/- sqrt(4 -2))/2

= 1 +/- sqrt(2)/2