finding the limits

Question

A subway train travels from one station to the next in 2 minutes. Its distance in Km, from the first station after (t) minutes is s(t)= t^2 - 1/3t^3. At what time will the train have a velocity of 0.5km/min. 

Answer 1

s(t) = t² - (1/3)t³ = distance traveled by the train in t minutes.

 

s'(t) = 2t - t² = velocity at time t

 

2t - t² = 0.5

 

2t² - 4t + 1 = 0

 

Use the quadratic formula to obtain the desired value of t.