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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics2. motion in straight line1 Mark
MCQ
A train starts from rest from a station with acceleration $0.2 \,m / s ^2$ on a straight track and then comes to rest after attaining maximum speed on another station due to retardation $0.4 \,m / s ^2$. If total time spent is half an hour, then distance between two stations is [Neglect length of train]
  • ✓
    $216$
  • B
    $512$
  • C
    $728$
  • D
    $1296$
✓

Answer

Correct option: A.
$216$
a
(a)

Shortcut : $S=\frac{1}{2} \frac{\alpha \beta}{\alpha+\beta} T^2$

$\alpha \rightarrow$ Acceleration

$\beta \rightarrow$ Deceleration (magnitude only)

$T \rightarrow$ Time of journey

$S \rightarrow$ Distance travelled

Given, $\alpha=0.2 \,ms ^{-2}$

$\beta=0.4 \,ms ^{-2}$

$T=$ half an hour $=30 \times 60 \,s =1800 \,s$

$S=\frac{1}{2} \times\left(\frac{0.2 \times 0.4}{0.2+0.4}\right) \times(1800)^2$

$\Rightarrow S=216000 \,m$

$\Rightarrow S=216 \,km$

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