A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a…

A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance $\mathrm{s}_{1}$ in the first 10 seconds and distance $\mathrm{s}_{2}$ in the next 10 seconds, then
  1. $\mathrm{s}_{2}=\mathrm{s}_{1}$
  2. $\mathrm{s}_{2}=2 \mathrm{~s}_{1}$
  3. $\mathrm{s}_{2}=3 \mathrm{~s}_{1}$
  4. $\mathrm{s}_{2}=4 \mathrm{~s}_{1}$

Solution

Let a be the constant acceleration of the particle. Then $\mathrm{s}=\mathrm{u} \mathrm{t}+\frac{1}{2} \mathrm{a} \mathrm{t}^{2}$
$\mathrm{s}_{1}=0+\frac{1}{2} \times \mathrm{a} \times(10)^{2}=50$
and $\mathrm{s}_{2}=\left[0+\frac{1}{2} \mathrm{a}(20)^{2}\right]-50 \mathrm{a}=150 \mathrm{a}$
$\therefore \mathrm{s}_{2}=3 \mathrm{~s}_{1}$ *

Asked in: JEE Mains - Motion In One Dimension - Test 2

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