Instantaneous Acceleration

Definition:

$$\vec{a}$$ $$\equiv$$ $$\lim_{\Delta t \rightarrow 0}^{}$$$${\frac{\vec{v}}{\Delta t}}$$

Note: a particle can accelerate in different ways:

1.

The magnitude of $\vec{v}$ can change in time, while the direction of motion stays the same.

2.

The magnitude of $\vec{v}$ , |$\vec{v}$| , can stay constant, while the direction of motion changes. This only happens in more than one dimension. We will discuss this further in Chapter 7.

3.

Both |$\vec{v}$| and the direction of $\vec{v}$ can change.