A man running with a uniform speed 'u' on a straight road observes a stationary bus at a distance 'd' ahead of him. At that instance , the bus starts with an acceleration 'a' .The condition that he would be able to catch the bus is:

d \leq \frac{u^{2}}{a}

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d \leq \frac{u^{2}}{2 a}

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d \leq \frac{u^{2}}{3 a}

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d \leq \frac{u^{2}}{4 a}

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Solution

The correct option is B $d \leq \frac{u^{2}}{2 a}$
Relative speed of man w.r.t bus $= u$
and acceleration w.r.t bus $= - a$
if man catch the bus
$d \leq x$ where x is calculated as
$v^{2} - u^{2} = - 2 a x$
$v =$ final velocity w.r.t bus that is zero.
$0 - u^{2} = - 2 a x$
$x = \frac{u^{2}}{2 a}$
hence $d \leq \frac{u^{2}}{2 a}$

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A man running with a uniform speed 'u' on a straight road observes a stationary bus at a distance 'd' ahead of him. At that instance , the bus starts with an acceleration 'a' .The condition that he would be able to catch the bus is:

The correct option is B d≤u22aRelative speed of man w.r.t bus =u and acceleration w.r.t bus =−aif man catch the bus d≤x where x is calculated asv2−u2=−2axv= final velocity w.r.t bus that is zero.0−u2=−2ax x=u22ahence d≤u22a