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.

Options

A. `- 3.5 m//s^(2)`
B. `-7m//s^(2)`
C. `-15 m//s^(2)`
D. `-30 m//s^(2)`

Answer

A

Explanation

v = `sqrt (180 - 7s)` 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)`