Contextual Applications of Differentiation

A particle's position is given by $x(t) = t^3 - 6t^2 + 9t$. During what time interval is the particle moving to the right?

The temperature of a room is changing at a rate of $T'(t) = 2t - 5$ degrees Celsius per minute, where $t$ is in minutes. What are the units of the derivative $T'(t)$?

Water is leaking from a tank at a rate of $R(t) = 50 - t^2$ liters per hour, where $t$ is in hours and 0 \le t \le 5. How much water leaks out of the tank during the first 3 hours?

If the position of a particle is given by $x(t) = t^2 + 3t - 5$, what is the velocity of the particle at $t = 2$?

A particle moves along the x-axis with position given by $x(t) = t^3 - 6t^2 + 5$ for 0 \le t \le 5. What is the maximum speed of the particle on this interval?

The rate of change of the population of a town is modeled by the function $P'(t)$, where $t$ is measured in years. What does $P'(5) = 200$ mean?