Final answer:
Acceleration is defined as the second derivative of the position function with respect to time, making it the result of taking the derivative of the velocity function.
Step-by-step explanation:
Acceleration is the rate at which velocity changes, and it can be obtained from the derivative with respect to time of the velocity function. Since velocity is the derivative of the position function (position to velocity to acceleration), acceleration can also be defined as the second derivative of the position function with respect to time. This means that acceleration is the result of differentiating the distance (or position) function twice, once to get velocity and a second time to get acceleration.
Instantaneous acceleration is a vector quantity and can be found by taking the derivative of the velocity function with respect to time. In three dimensions, acceleration, a(t), can be expressed as a vector sum of the accelerations along the x-, y-, and z-axes. For projectile motion near Earth's surface, acceleration due to gravity is constant and affects the motion of the object.