Question

A particle moves along the X-axis with velocity $v=\frac{dx}{dt}=f\left(x\right)$ then the acceleration of the particle is?

• A. $f^{\prime \prime }\left(x\right)$
• B. $f\left(x\right)$
• C. $f\left(x\right)\cdot f^{\prime }\left(x\right)$
• D. $f^{\prime }\left(x\right)$

Answer 1

The correct option is A $f^{\prime \prime }\left(x\right)$

We know that

$V=\frac{dx}{dt}=f\left(x\right)$

On differentiating we have

$\frac{dv}{dt}=\frac{d\left(f\right(x\left)\right)}{dx}\times \frac{dx}{dt}$

$=f^{\prime }\left(x\right).f\left(x\right)$