Question

Write the equation of motion. What does each letter indicate?

Answer 1

Hint: If the body changes its position with time it is said to be moving else it is at rest. Motion is always relative to the observer. Motion is the combined property of the object under the observer. There is no meaning of rest or motion without a viewer. In other words, absolute motion or rest is meaningless.

Complete step by step solution:
There are three equations of motion:
$v=u+at$
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
${{v}^{2}}={{u}^{2}}+2as$
where, $v=$ final velocity
              $u=$ initial velocity
              $a=$ acceleration
               $t=$ time taken
               $s=$ displacement
If a body starts from rest and moves with uniform acceleration, then distance covered by the body in $t$seconds is proportional to ${{t}^{2}}$. So, we can say that the ratio of distance covered in $1$ sec, \[2\]sec and \[3\]sec is $1:4:9$.
If a body starts from rest and moves with uniform acceleration, then distance covered by the body in $nth$ second is proportional to ($2n-1$).
So, we can say that the ratio of distance covered in the first sec, second sec and third sec will be \[1:3:5\].
A body moving with a velocity $u$ is stopped by the application of brakes after covering a distance $s$. If the same body moves with the velocity $nu$ and the same braking force is applied on it, then it will come to rest after covering some distance of ${{n}^{2}}s$. As ${{v}^{2}}={{u}^{2}}-2as$

Note:
One should keep in mind while solving turning questions of kinematics that whether distance is asked or displacement. If displacement is asked then its go through the above formulas but if distance is asked then first of all you have to check whether at some instant during the entire motion velocity is becoming zero or not, because in case of displacement we only calculate the difference between final position and initial position but in case of distance you need to calculate the length of whole path.