Why calculus
Calculus is the study of how functions change. In Physics, you learned that an object whose position is changing is moving, and therefore has velocity (speed with direction). If it moves farther in a given amount of time, it is going faster than if it moves less in the same amount of time. Conversely, we know that if an object is moving at a certain speed for a given amount of time, we can calculate the change in its position (distance traveled). So not only can we relate change in position to , we can reverse the process and find out about when we know . Calculus ties these two things together and gives us tools to analyze them in both "directions
The red graph represents the object's position during the time interval from 0 to 10 seconds. The blue graph represents the velocity of the object. Remember that "velocity" is the same as the rate of change of the position: an object moving at a speed of 3 m/s is changing its position at a rate of 3 m every second
First, note how the slope of the position graph always matches the height of the velocity graph. Then notice how the area under the velocity graph always matches the position of the ball (the ball's initial position is zero). When the ball rises,both its position and its velocity are positive. When the ball falls, its position is still positive (still above ground), but its velocity (slope of position) is negative (since it is moving down).