Activity 10.7.2

In this activity, we will work to understand the sign of $a_{\vT}$ and $a_{\vN}$.

1. The tangential component of acceleration is defined as $a_{\vT} = \va \cdot \vT$, while equation this equation establishes that $a_{\vT} = \frac{d\text{(speed)}}{dt}$ is also true. Use these formulas to determine whether $a_{\vT}$ can be zero. Either explain why $a_{\vT}$ is always nonzero or describe scenarios in which $a_{\vT}=0$.

2. Determine whether $a_{\vT}$ can be negative. Either explain $a_{\vT}$ is never negative or describe scenarios in which $a_{\vT}\lt 0$

3. The normal component of acceleration is defined as $a_{\vN} = \va \cdot \vN$, while equation this equation establishes that $a_{\vN} = (\text{speed}) \vecmag{\frac{d\vT}{dt}}$ is also true. Use these formulas to determine whether $a_{\vN}$ can be negative. Either explain why $a_{\vN}$ is negative or describe scenarios in which $a_{\vN}\lt 0$.

4. Determine whether $a_{\vN}$ can be zero. Either explain why $a_{\vN}$ is always nonzero or describe scenarios in which $a_{\vN}=0$.