Correct Answer - Option 2 : S
2 = 3s
1
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, g = Acceleration due to gravity, t = time, and h = height/Distance covered
CALCULATION:
Given Initial velocity u = 0 m/s
- We know that when the force is constant, the acceleration is also constant.
The second equation of motion is given as,
\(⇒ S=ut+\frac{1}{2}at^{2}\)
For time t,
⇒ displacement S = S1,
\(⇒ S_{1}=(0\times t)+\frac{1}{2}at^{2}\)
\(⇒ S_{1}=\frac{1}{2}at^{2}\) ------- (1)
For total time 2t,
⇒ displacement S = S1+S2,
\(⇒ S_{1}+S_{2}=(0\times 2t)+\frac{1}{2}a(2t)^{2}\)
\(⇒ S_{1}+S_{2}=4\frac{1}{2}at^{2}\) ------- (2)
By equating equation 1 and equation 2, we get
\(⇒ S_{1}+S_{2}=4S_{1}\)
\(⇒S_{2}=3S_{1}\)
- Hence, option 2 is correct.