Applications in Science and Engineering
Lots of fields can benefit from the concepts in calculus. In cases where relationships can be graphed, calculus can be used. That's the only prerequisite.
How fast is a diver or a long jumper going upon impact (or at any point during the dive or jump). What path does a gymnast follow when she releases the uneven bars? How long does it take for a car to drive from Point A to Point B?
All of these questions can be answered using calculus.
In a graph of distance vs. time, velocity is derivative. Derivatives describe the rate of change at points on a graph so this shouldn't be too much of a surprise. If we had to describe the rate of change of someone's position, velocity or speed would be a pretty apt description.
When chemicals react with one another, calculations about the rates at which they react involve calculus. Engineers might use calculus for optimization problems. For instance, they can find the largest volume that can be held by a soda and/or pop can, while using the smallest possible amount of aluminum. They can also figure out the best size can top and bottom for optimal stacking ability.
Video game engineers might use various forms of calculus to simulate real-life situations. Depending on the angle that a force is applied, where should those angry birds land after sling-shot release? Will the pigs pay? Video games are steeped in calculus simulations.