Correct Answer - Option 2 : 1 : 3
CONCEPT:
Equation of Kinematics:
- These are the various relations between U, V, a, t, and s for the particle moving with uniform acceleration where the notations are used as:
- Equations of motion can be written as
⇒ V = U + at
\(⇒ s =Ut+\frac{1}{2}{at^{2}}\)
⇒ V2 = U2+ 2as
where, U = Initial velocity, V = Final velocity, a = Acceleration, t = time, and h = Distance covered
CALCULATION:
Given U = 0 m/sec
Let the acceleration be a.
By the second equation of motion, the distance covered in the first 10 sec is given as (s10 = x),
\(⇒ s_{10} =0\times10+\frac{1}{2}{\times a\times10^{2}}\)
⇒ x = 50a -----(1)
The distance covered in the next 10 sec is given as (s2 = y),
⇒ y = Distance covered in first 20 sec - Distance covered in first 10 sec
⇒ y = s20 - s10 -----(2)
By the second equation of motion, the distance covered in the first 20 sec is given as,
\(⇒ s_{20} =0\times10+\frac{1}{2}{\times a\times20^{2}}\)
⇒ s20 = 200a -----(3)
By equation 1, equation 2, and equation 3,
⇒ y = 200a - 50a
⇒ y = 150a -----(4)
By equation 1 and equation 4,
\(\Rightarrow \frac{x}{y}=\frac{50a}{150a}\)
\(\Rightarrow \frac{x}{y}=\frac{1}{3}\)
- Hence, option 2 is correct.