Tony's Cart

Tony is a driver of the Fastpass cart in the animal kingdom section of Funworld. He needs to drive the cart at a constant speed so that the customer can see the animals clearly. Before the cart reaches the constant speed, its velocity varies.

What is known:

• The cart starts from rest.
• The velocity varies as a function of time,
  v = 2500 t^2/3 mile/hour
  where t is in hours.
• The final constant speed of the cart is 10 mile/hour.

How long does it take the cart to reach the required speed?

When the velocity is positive, the function of speed is a one-to-one function.