Question

A particle moving with uniform acceleration has its final velocity $(v=\sqrt{150+8x})m/s$ where $x$ is the distance travelled by the body. Then the acceleration is

• A. $+4m/s^2$
• B. $-4m/s^2$
• C. $+8m/s^2$
• D. $-8m/s^2$

Answer 1

Answer: (A)

$+4m/s^2$

$v=\sqrt{150+8x}$

$v^2=150+8x$

$\frac{d}{dt}\left(v^2\right)=\frac{d}{dt}(150+8x)$

$2v\frac{dv}{dt}=\frac{d}{dt}\left(8x\right)=8\frac{dx}{dt}=8v$

$\frac{dv}{dt}=\frac{8}{2}=4=a$.