List some examples of acceleration.

Acceleration

1. Acceleration is defined as the rate of change of velocity with respect to time.
2. If $v$ is the velocity and $t$ is the time then instantaneous acceleration is given as $a_{int}=\frac{dv}{dt}$.
3. If $v_1$ is the initial velocity and $v_2$ is the final velocity is a total time period $T$, then the average acceleration is given as $a_{avg}=\frac{v_2-v_1}{T}$.
4. Therefore, the unit of acceleration is $m/s^2$.
5. Since velocity is a vector quantity, acceleration is also a vector quantity.
6. The product of acceleration undergone by the body and its mass gives the value of force applied by the body.
7. If $S$ is the displacement of the body, the acceleration can also be expressed as, $a_{int}=\frac{dv}{dt}=\frac{d}{dt}\left(\frac{dS}{dt}\right)=\frac{d^{2}S}{d{t}^2}$.

Examples of Acceleration

1. For a body in a uniform circular motion, even though its speed remains constant, its direction is constantly changing. This causes a constant change in velocity that results in the generation of acceleration.
2. For a body that starts to move, it increases its velocity from $v_1=0$, since it is initially at rest to a final velocity $v_2$. Hence it undergoes acceleration.
3. Similarly, for a moving body that comes to rest, it decreases its velocity from $v_1$ to $v_2=0$. Hence it undergoes a negative acceleration, retardation, or deceleration.
4. A freely falling body is acted upon by acceleration that occurs due to the gravitation attractive force of the earth.