Question bank/JEE Main/Physics

A street car moves rectilinearly from station A (here car stops)
to the next station B (here also car stops) with an acceleration varying
according to the law f = a - bx, where a and b are positive constants
and x is the distance from station A. The distance between the two
stations & the maximum velocity are
$x = \frac{na}{b};v_{\max} = \frac{na}{2\sqrt{b}}$. Find n

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f = a - bx means particle will do SHM.
At mean position; f = 0
[IMAGE] In the figure shown, 'C' is the mean position and A & B are extreme
positions

Source: Grass-G / P-09 Physics paper 26 October.docx