Question

True or False The acceleration of a particle is the second derivative of the position function. Justify your answer.

Short answer

Yes, it is true that the acceleration of a particle is the second derivative of the position function. This is because acceleration is the rate change of velocity, which is already the rate of change of the position.

Step-by-step solution

Physics Definitions

First, it's fundamental to understand the definitions of position, velocity, and acceleration. The position of an object refers to its location at a certain point of time. Velocity describes the rate of change of the position over time, it essentially is the speed and direction. Acceleration, on the other hand, is the rate of change of velocity over time.

Mathematical Relation

In calculus, the rate of change of a function is represented by its derivative. Therefore, the velocity (which is the rate of change of position) will be the first derivative of the position function, and acceleration (which is the rate of change of velocity) will be the derivative of the velocity function.

Final Explanation

By connecting those concepts, we can assert that the acceleration, being the rate of change of velocity (which is already the rate of change of position), is indeed the second derivative of the position function.