Question

18. A body moving with uniform retardation covers 3 km before its speed is reduced to half of its initial vall
comes to rest in another distance of
1 km
(2) 2 km
km
(3) 3 km
(4)1/2

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Answer 1

First case:

$let \\ initial \: velocity = x \\ final \: velocity = \frac{x}{2} \\retardation = a \\ given \: \\distance = 3 \: km \\ {v}^{2} - {u}^{2} = 2as \\ { (\frac{x}{2}) }^{2} - {x}^{2} = 6a \\ \frac{ - 3 {x}^{2} }{4} = 6a \: \: \: \: eq1$

Second case:

$initial \: velocity = \frac{x}{2} \\ fina \: velocity \: = 0 \\ retardation = a \\ distance = s \: km \\ {v}^{2} - {u}^{2} = 2as \\ 0 - { (\frac{ x }{2}) }^{2} = 2as \\ \frac{ { - x}^{2} }{4} = 2as \: \: \: eq \: 2$

$\frac{eq \: 1}{eq \: 2} = \frac{ \frac{ - 3 {x}^{2} }{4} }{ \frac{ { - x}^{2} }{4} } = \frac{6a}{2as} \\ 3 = \frac{3}{s} \: \\ s = 1km$