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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/s2
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B
-7 m/s2
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C
-15 m/s2
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D
-30 m/s2
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Solution

The correct option is C - 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, 
$$v^2=u^2+2as\\ \Longrightarrow {(\sqrt{180-7x})}^2=u^2+2as\\ \Longrightarrow 180-7x=u^2+2ax$$

On comparing both sides, $$u^2=180$$ and $$2a=-7$$
$$\Longrightarrow a=-3.5m/s^2$$

Physics

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