Acceleration

Definition: Average acceleration is the change in velocity over the change in time:
 

$$\bar{a} \equiv {\frac{\Delta v}{\Delta t}} {\frac{v_f - v_i}{t_f-t_i}}$$ (5)

Definition: Instantaneous acceleration is calculated by taking shorter and shorter time intervals, i.e. taking $\Delta$t $\rightarrow$ 0:
 

$$\equiv \lim_{\Delta t \rightarrow 0}^{} {\frac{\Delta v}{\Delta t}}$$ (6)

Note:

• Acceleration is the rate of change of velocity.
• When velocity and acceleration are in the same direction, speed increases with time. When velocity and acceleration are in opposite directions, speed decreases with time.
• Graphical interpretation of acceleration: On a graph of v versus t , the average acceleration between P and Q is the slope of the line between P and Q, and the instantaneous aceleration at P is the tangent to the curve at P.
• From now on ``velocity'' and ``acceleration'' will refer to the instantaneous quantities.