**Acceleration** is the rate at which speed increases or decreases. Acceleration involves a changes in speed or a change in velocity during a time interval. Acceleration can be both a scalar quantity and a vector quantity. It is a scalar quantity when we consider only its magnitude. If we also indicate the direction in which a moving object is accelerating, then we are defining acceleration as a vector quantity.

When an object slows down we say it is decelerating. Deceleration (many teachers don't like to use this term) is really negative acceleration. The symbol for acceleration is a . The units for acceleration are [m/s^{2 }] {"meters-per-second-squared"}.

"a" with no arrow on top = scalar acceleration; (with the arrow on top) = vector acceleration

Acceleration over a definite time interval is known as **average acceleration**. Acceleration calculated at each instant (very small time segment) along the path of motion of a moving object is known as **instantaneous acceleration**.

The equation for average acceleration is :

Note that is the change in speed or velocity during the time interval (change in time) . This means that if at time t_{1} the speed of an object was v_{1}, at a later time t_{2}, its corresponding speed is v_{2}.

[Tip: The symbol ("delta") is a mathematica operatpor that indicates "a Final quantity - an Initial quantity".

[Your textbook or teacher may use the subscripts "i" for initial and "f"" for final ... this site uses "1" for initial and "2" for final]

**Example:**

A police car is cruising at 50 km/h along a straight road. A motorist zooms past the cruiser. The police officer steps on the gas and catches up to the speeding car 30 s later at that instant her speedometer was reading 80 km/h.

What was the *average acceleration* of the police car during the 30 s?

**Given:** v_{1} = 50 km/h v_{2} = 80 km/h

let the initial time t _{1 }= 0 then, t _{2} = 30s

**Find:** a_{av}

**Solution:**

The standard unit for acceleration is the m/s^{2} . Therefore we will convert our answer () to m/s^{2} .

1 km = 1000 m and 1 h = 3600 s Therefore:

**The police cruiser accelerated at 0.28 m/s ^{2}**