Question

A body moving with some initial velocity and having uniform acceleration attains a final velocity $ v \,m/s $ after travelling $ x\, m $ . If its final velocity is $ v=\sqrt{180-7x} $ , find the acceleration of the body.

• A. $ -3.5\,m/s^{2} $
• B. $ -7.5\,m/s^{2} $
• C. $ -15\,m/s^{2} $
• D. $ -30\,m/s^{2} $

Answer 1

Answer: (A)

$ v=\sqrt{180-7x} $ where $ x $ is the distance,
$ \therefore v^{2}=180-7x $
From the dimensions, $ 180 $ has dimensions of square of velocity.
For a body travelling with uniform acceleration,
$ v^2 - u^2 = 2aS $ is valid. By inspection one can say
$ u^2 = 180 $ , $ 2aS = -7x $ . (here $ S = x) $
$ -7x=2ax $ .
$ \therefore a=-3.5\,m/s^{2} $