The acceleration function is the derivative of the position function.Group of answer choicesTrueFalse

Understanding the Question

The question asks whether the statement "The acceleration function is the derivative of the position function" is true or false. To analyze this, we need to clarify the relationships between position, velocity, and acceleration in terms of derivatives.

Relevant Concepts

1. Position Function $s(t)$: Represents the position of an object at time $t$.
2. Velocity Function $v(t)$: The derivative of the position function: $v(t) = \frac{ds}{dt}$
3. Acceleration Function $a(t)$: The derivative of the velocity function: $a(t) = \frac{dv}{dt} = \frac{d^2s}{dt^2}$

Analysis

• The position function $s(t)$ leads to the velocity function $v(t)$ via the first derivative.
• The acceleration $a(t)$ is derived from the velocity function, which means it is the second derivative of the position function $s(t)$.

Conclusion

Given this understanding, the statement that "The acceleration function is the derivative of the position function" is False.

Final Answer

False. The acceleration function is actually the second derivative of the position function, not the first derivative.