Question

A body moving with some initial velocity and having uniform acceleration attains a final velocity $v\ m/s$after travelling $x\ m$. If the 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

Hint: We know that relation between initial velocity, final velocity, distance travelled and acceleration of the body can be given by the formula, ${{v}^{2}}-{{u}^{2}}=2as$. Using this formula, we will find the acceleration of the body in terms of $m/{{s}^{2}}$

Formula used: ${{v}^{2}}-{{u}^{2}}=2as$

Complete step-by-step answer:
In the question it is given that a body moving with some initial velocity and having uniform acceleration attains a final velocity $v\ m/s$ after travelling $x\ m$. If the final velocity is $v=\sqrt{180-7x}$ and we have to find the acceleration of the body, so, first of all the relation between relation between initial velocity, final velocity, distance travelled and acceleration of the body can be given by the formula,
${{v}^{2}}-{{u}^{2}}=2as$ ………..(i)
Where, v is final velocity, u is initial velocity, a is acceleration of the body and s is the distance covered by the body.
Now, here it is given that the body travels $x\ m$ and attains the final velocity as $v=\sqrt{180-7x}$
So, it can be seen mathematically as,
$s=x\ m$
$v=\sqrt{180-7x}\ m/s$ ……………(ii)
On, squaring the expression (ii) on both the sides we will get,
${{v}^{2}}=180-7x$………….(iii)
Now, equation (i) can also be written as,
${{v}^{2}}={{u}^{2}}+2ax$ ……………(iv)
On comparing equation (iii) and (iv), it can be said that value of ${{u}^{2}}$is 180 and $2ax=-7x$,
$a=\dfrac{-7}{2}=-3.5\ m/{{s}^{2}}$.

Note: Students might make mistakes in considering the initial velocity as 180 from expression (iii) and instead of that they equate the whole equation and find the solution but it will consume more time and final answer may also vary so students should take care while solving such problems.