Question: How do you find the magnitude of acceleration of a particle?...

Question

How do you find the magnitude of acceleration of a particle?

Answer 1

Solution

The rate of change of velocity is called acceleration. It is a vector quantity; this means it has both magnitude as well as acceleration. Magnitude is represented by units. Acceleration depends on various parameters like time, velocity, force etc. It can be translational or rotational.

Complete answer:
The change in velocity that takes place per unit time is called acceleration. Its SI unit is $m{{s}^{-2}}$ . It is given by-
$a=\dfrac{v-u}{t}$
Here, $a$ is the acceleration
$v$ is final velocity
$u$ is the initial velocity
$t$ is the time taken
The magnitude of acceleration is represented by its unit and the direction is represented by a unit vector. In order to calculate the magnitude we can use formulas and relations. The above equation can be used to calculate the magnitude of acceleration using velocity and time.
We know that the product of mass and acceleration is called force. It is given by-
$F=ma$ - (1)
Here, $F$ is the force applied
$m$ is mass of the body
$a$ is the acceleration
From eq (1), we can calculate acceleration as-
$a=\dfrac{F}{m}$
The equations of motion in one dimension can also be used to calculate the magnitude of acceleration, when magnitude is constant. There are three equations of motion, they are-
$\begin{aligned} & v=u+at \\\ & {{v}^{2}}={{u}^{2}}+2as \\\ & s=ut+\dfrac{1}{2}a{{t}^{2}} \\\ \end{aligned}$
Here, $v$ and $u$ are initial and final velocities respectively.
$a$ is the acceleration
$s$ is the displacement
$t$ is the time taken
Therefore, the magnitude of acceleration is the quantity represented by the unit. It can be calculated by using various relations between acceleration and other parameters like velocity, force etc.

Note:
According to Newton’s second law, the acceleration is non-zero if an external force is being applied, otherwise it is zero. Acceleration can be varying or constant. The most commonly used unit for acceleration is its SI unit. Acceleration is used to describe motion of a body and determine the force.