Speed, Velocity, and Acceleration</div>

Acceleration

How will you compare traveling along a highway with very light traffic, with traveling along a street with heavy traffic? Note if the vehicle you are riding in has constant or changing velocity. You may observe that, as your vehicle passes a street with heavy traffic, it slows down and changes its velocity. The rate of change in velocity is called acceleration. Since velocity involves speed and direction, acceleration also involves a change in either speed or direction, or both.

Acceleration, symbolized by $\overrightarrow{a}$ , is the change in velocity divided by the change in time; hence

\[ \text{acceleration} = \frac{\text{change in velocity}}{\text{change in time}} \quad \text{or} \quad \overrightarrow{a} = \frac{\Delta \overrightarrow{v}}{\Delta t} \]

\[ \text{acceleration} = \frac{\text{final velocity} - \text{initial velocity}}{\text{final time} - \text{initial time}} \quad \text{or} \quad \overrightarrow{a} = \frac{v_f - v_i}{t_f - t_i} \]

When the final velocity is greater than the initial velocity, the acceleration is positive. This means that the body moved at a faster rate. When the final velocity is less than the initial velocity, the acceleration is negative, and the body moved at a slower rate. When the body’s velocity varies in a uniform way with time, it is called constant acceleration.