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 $m/s^2$
• C. -15 $m/s^2$
• D. -30 $m/s^2$

Answer 1

Answer: (A)

- 3.5 $m/s^2$

Let initial velocity $=u$ and $a\text{(uniform acceleration)},v=\sqrt{180-7x}$

$x=\text{distance traveled}$

By applying third equation of motion,

$v^2=u^2+2as⟹{\left(\sqrt{180-7x}\right)}^2=u^2+2as⟹180-7x=u^2+2ax$

On comparing both sides, $u^2=180$ and $2a=-7$

$⟹a=-3.5m/s^2$