First slide

Displacement in nth sec

Question

Three particles move in a straight line with initial velocities $v_{1}, v_{2} a n d v_{3} (v_{1} < v_{2} < v_{3})$ each with constant retardation ‘a’ such that the motion continues for more than one second before velocity of each particle becomes zero. If $s_{1}, s_{2} a n d s_{3}$ respectively be the distances travelled in the last one second before velocity becomes zero, then

Moderate

A

$s_{1} = \frac{v_{1}^{2}}{2 a}, s_{2} = \frac{v_{2}^{2}}{2 a}, s_{3} = \frac{v_{3}^{2}}{2 a}$
B

$s_{1} > s_{2} > s_{3}$
C

$s_{1} = s_{2} = s_{3}$
D

$s_{1} < s_{2} < s_{3}$

Solution

$\begin{array}{l} S_{1} = v_{1} - a (n - 1 / 2) \\ O = v_{1} - a t \\ t = \frac{v_{1}}{a} \\ S_{1} = v_{1} - a [\frac{v_{1}}{a} - 1 / 2] \\ S_{2} = v_{2} - a (\frac{v_{2}}{a} - 1 / 2) \\ S_{3} = v_{3} - a (\frac{v_{3}}{a} - 1 / 2) \\ S_{1} = S_{2} = S_{3} \end{array}$

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