Before calculus you probably took a class where you did lines (slope/intercept form, etc), right? Think about all the word problems where you wanted to know the slope of the line- when you wanted to know "rate of change" or "how much more it costs to build one more object" or anything like that. All of those types of problems require calculus if you want to do them for anything more complicated than a line.

As an example- perhaps you had a problem like this:

> A car is traveling down a race track in a straight line. At t=10 seconds it's 100 meters down the track, and at t = 20 seconds it's 150 meters down the track, how fast is it traveling? Where did it start on the track?"

So, you find the slope and intercept of the equation, and say "oh, it's traveling at 5 m/s, and it started 50 m down the track.

But if the car isn't traveling at a constant velocity, instead you say "at t = 0 seconds a car starts from rest and is 100 m down the track. At t = 10 seconds, he's 200 meters down the track, and he was accelerating the entire time. How fast is it traveling 2 seconds after it starts to accelerate?" well now you need to use calculus. You need to find the slope of the tangent line to the equation that describes his position. You hear physics terms a lot because in general, velocity is the derivative of position, and acceleration is the derivative of velocity (aka- the tangent line to the position graph is the velocity, and the tangent line to the velocity graph is the acceleration, just like the slope of a line in a linear graph is the velocity).