A student is standing at a distance of 50metres from the bus. As soon as the bus begins its motion with an acceleration of 1 ms –2 , the student starts running towards the bus with a uniform velocity \(\mu\) . Assuming the motion to be along a straight road, the minimum value of \(\mu\) , so that the student is able to catch the bus is
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Let student will catch the bus after t sec . So it will cover distance ut .
Similarly distance travelled by the bus will be \(\frac{1}{2} \alpha^{2}\) for the given condition
\(ut - 50 + \frac{1}{2}at^{2} - 50 + \frac{t^{2}}{2}\) [ \(a = 1 \, m/s^{2}\) ]
⇒ ⇒ u \(-\frac{50}{t} + \frac{\tau}{2}\)
To find the minimum value of u
\(\frac{d\vec{u}}{dt} = 0\) , so we get \(t = 10 \text{ sec}\) , then \(u \quad 10 \, m/s\)
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