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2. motion in straight line — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics2. motion in straight line1 Mark
MCQ
A particle starts moving from rest in a straight line with constant acceleration. After time $t_0$, acceleration changes its sign (just opposite to the initial direction), remaining the same in magnitude. Determine the time from the beginning of motion in which the particle returns to the initial position.
  • A
    $2 t_0$
  • ✓
    $(2+\sqrt{2}) t_0$
  • C
    $3 t_0$
  • D
    $(2-\sqrt{2}) t_0$
✓

Answer

Correct option: B.
$(2+\sqrt{2}) t_0$
b
(b)

Taking, $s=u t+\frac{1}{2} a t^2$, from point $B$ onwards we have,$-\frac{1}{2} a t_0^2=\left(a t_0\right) t-\frac{1}{2} a t^2$

$\therefore \quad t^2-2 t_0 t-t_0^2=0$

$\therefore \quad t=\frac{2 t_0 \pm \sqrt{4 t_0^2+4 t_0^2}}{2}=\left(t_0+\sqrt{2} t_0\right)$

$\therefore \quad \text { Total time }=t_{A B}+t=(2+\sqrt{2}) t_0$

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