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 instant, 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 $d \leq \frac{u^{2}}{2 a}$
Let the man meet the bus at time t.
Velocity of the man be u, acceleration of the bus be a, then
$u t = \frac{1}{2} a t^{2} + d$
For the time to be positive, the discriminant of the above expression should be greater than or equal to zero.
Required condition $d \leq \frac{u^{2}}{2 a}$

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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 instant, 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≤u22aLet the man meet the bus at time t. Velocity of the man be u, acceleration of the bus be a, then ut=12at2+d For the time to be positive, the discriminant of the above expression should be greater than or equal to zero. Required condition d≤u22a