Kinematics

In mechanics acceleration is the rate of change of velocity over time. Since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. Therefore a body accelerates if there is a change to the magnitude or direction of its velocity.

If a human body decreases its velocity, increases its velocity, or changes the direction of its motion, it moves with acceleration.

The average acceleration is the ratio between the change to velocity and the time interval:

where a is average acceleration, Δv is change of velocity, v_k is final velocity, v_p is initial velocity and Δt is the time interval.

From this formula it is obvious that acceleration can have both negative and positive values. Negative acceleration is called deceleration (the velocity of the body is decreasing). In SI units, acceleration is measured in meters per second squared (m/s²).

If the length of the time intervals in which we measure acceleration approaches zero, the resultant value is instantaneous acceleration. Instantaneous acceleration is the acceleration in a very short interval of time as Δt approaches zero.

Since acceleration is a vector, just as velocity and displacement are, it can be resolved in space into three components of acceleration. Vector of instantaneous acceleration, however, has a unique feature compared to vector of instantaneous velocity:

The direction of the vector of instantaneous acceleration is not always identical to the direction of the body’s motion.

When you start running, your acceleration has the same direction as your motion. When you start slowing down, your acceleration has exactly the opposite direction to the direction of your motion. In curvilinear motion with constant velocity (uniform curvilinear motion), instantaneous acceleration has also different direction from the direction of motion itself (e.g. a cyclist on a velodrome). And one more important example: if you are running with constant velocity (both the magnitude and direction of your velocity are constant), your acceleration has no direction because it equals zero.