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2.Motion in Straight Line
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A train starting from rest travels the first part of its journey with constant acceleration $a$ , second part with constant velocity $v$ and third part with constant retardation $a$ , being brought to rest. The average speed for the whole journey is $\frac{{7v}}{8}$. The train travels with constant velocity for $...$ of the total time
A
$0.75$
B
$0.87$
C
$0.83$
D
$1.28$
Solution
$\mathrm{v}_{\mathrm{av}}=\frac{\mathrm{v}_{\max } \mathrm{t}+\mathrm{v}_{\mathrm{vax}}(\mathrm{T}-2 \mathrm{t})}{\mathrm{T}}=\frac{7}{8} \mathrm{v}_{\max }$
$t+T-2 t=\frac{7}{8} T$
Time when particle move with constant velocity $=T-2 t=3 / 4 T$
Standard 11
Physics
