First slide

Rectilinear Motion

Question

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:

Moderate

A

$5 {ms}^{- 1}$
B

$8 {ms}^{- 1}$
C

$10 {ms}^{- 1}$
D

$12 {ms}^{- 1}$

Solution

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

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