1. Tardigrade
  2. Question
  3. Physics
  4. A student is standing at a distance of 50 metres from a bus. As soon as the bus begins its motion (starts moving away from student) with an acceleration of 1 ms-2, the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is:

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Q. A student is standing at a distance of $50$ metres from a bus. As soon as the bus begins its motion (starts moving away from student) with an acceleration of $1 \,ms^{-2}$, the student starts running towards the bus with a uniform velocity $u$. Assuming the motion to be along a straight road, the minimum value of $u$, so that the student is able to catch the bus is:

Motion in a Straight Line

Solution:

$50 + x = ut ...(1)$ and $x = \frac{t^2}{2} \,...(2)$
image
From $(1)$ and $(2)$
$50 + \frac{t^2}{2} = ut$
$\Rightarrow t^2 - 2ut + 100 = 0$
For real roots, discriminant $= 0$
For minimum velocity, discriminant $= 0$
$\Rightarrow 4u^2 -400 = 0$
$ \Rightarrow u = 10 \,m/s$