Question

What are some examples of acceleration?

Answer 1

Hint: Here in order to give the examples of acceleration. We need to know properly the definitions of acceleration, velocity, distance and displacement.

Complete answer:
Distance is a numerical measurement of how far apart objects or points are. Distance is the total actual length that a particle travelled from its initial point. Displacement is the net length that the particle travelled between its initial and final points. Displacement can be equal, greater than or less than distance.

Velocity is a vector quantity; both magnitude and direction are needed to define it. The scalar absolute value also known as magnitude of velocity is called speed whose quantity is measured in the SI unit as metres per second$(m/s)$ or $(m\cdot {{s}^{-1}})$. The meaning of velocity of an object can be defined as the rate of change of the object’s displacement with respect to a frame of reference and time. It is a vector quantity, which means we need both magnitude and direction to define velocity.

Acceleration is the rate of change of velocity with respect to a frame of reference and time. It is a vector quantity, which means we need both magnitude and direction to define acceleration. Usually, acceleration means the change in speed, but not always. Acceleration is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time.
$Acceleration=\dfrac{Change\text{ }in\text{ }velocity}{time\text{ }taken}$
Its unit is $m/{{s}^{2}}$

There are three types of accelerated motions : uniform acceleration, non-uniform acceleration and average acceleration.
-An uniform accelerated motion object covers equal distances in equal intervals of time, irrespective of the duration of the time.
-A non-uniform accelerated motion object does not cover the same distance in equal time intervals, irrespective of the time interval duration.
-The average acceleration over a period of time is defined as the total change in velocity in the given interval divided by the total time taken for the change. For a given interval of time, it is denoted as ā.
Mathematically,
$\overrightarrow{a}=\dfrac{{{v}_{2}}-{{v}_{1}}}{{{t}_{2}}-{{t}_{1}}}=\dfrac{\Delta v}{\Delta t}$
Where ${v_2}$ and ${v_1}$ are the instantaneous velocities at time ${t_2}$ and ${t_1}$ and ā is the average acceleration.

Some uniform accelerated motion examples include a ball rolling down a slope, a skydiver jumping out of a plane, a ball dropped from the top of a ladder and a bicycle whose brakes have been engaged, train or any vehicle moving in a straight line applying a constant force,an object falling freely, movement of blades of a ceiling fan and such motions. Examples of non-uniform accelerated motion are circular motion of all types, a man driving in a random direction or with varying the race of his vehicle or both.

Note: The basic difference between uniform and non-uniform motion is that the uniform motion represents the motion in which the moving body covers the same distance in the same time, but in the case of non-uniform motion, the body travels unequal distances at the same time.