Question

If the displacement, velocity and acceleration of a particle at time, $t$ be $x, v$ and f respectively, then which one is true?

• A. $f = v^{3} \frac{d^{2}t}{dx^{2}}$
• B. $f = -v^{3} \frac{d^{2}t}{dx^{2}}$
• C. $f = v^{2} \frac{d^{2}t}{dx^{2}}$
• D. $f = -v^{2} \frac{d^{2}t}{dx^{2}}$

Answer 1

Answer: (B)

$\frac{d^{2} t}{d x^{2}}=\frac{d\left(\frac{d t}{d x}\right)}{d x}=\frac{d\left(\frac{1}{v}\right)}{d x} $
$=-\frac{1}{v^{2}} \frac{d v}{d t} \times \frac{1}{v}$
$\Rightarrow f=-v^{3} \frac{d^{2} t}{d x^{2}}$