Correct Answer - Option 3 : 1 ∶ 5
Concept:
Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
These equations are only valid when the acceleration of the body is constant and they move on a straight line.
There are three equations of motion:
\(v = u + at\)
\(s = ut + \frac{1}{2}a{t^2}\)
\({v^2} = {u^2} + 2as\)
Where, V = final velocity, u = initial velocity, s = distance travelled by the body under motion, a = acceleration of body under motion, and t = time taken by the body under motion
Calculation:
Given, a body starts from rest so, u = 0
We know that distance travelled equation is-
\(s = ut + \frac{1}{2}a{t^2}\)
Let the acceleration in the body is ‘a’ then the distance travelled in 1 sec is s1
\({s_1} = \frac{1}{2}a{t^2} = \frac{1}{2}a \times {\left( 1 \right)^2} = 0.5a\)
Let the acceleration in the body is ‘a’ then the distance travelled in 2 sec is s2
\({s_2} = \frac{1}{2}a{t^2} = \frac{1}{2}a \times {\left( 2 \right)^2} = 2a\)
In the 3 sec is –
\({s_3} = \frac{1}{2}a{t^2} = \frac{1}{2}a \times {\left( 3 \right)^2} = 4.5a\)
Distance travelled from 2 to 3 sec is -
\({s_3} -{s_2} = s\;\left( {in\;3\;sec} \right) - s\left( {in\;2\;sec} \right) = 4.5a-2a=2.5a\)
The ratio is-
\(\frac {s\;in\;1\;sec}{s\;in\;3\;sec}=\frac{{{s_1}}}{{{s_3}-{s_2}}} = \frac{{0.5}}{{2.5}} = \frac{1}{5}\)
Hence, the option is 1/3 is correct
