Question

A particle moves along the curve $y=a{x}^2$, with constant speed $v$. The acceleration at the origin of coordinates being $($ where $a$ is a constant $)$:

• A. $\frac{v^2}{2a}$
• B. $2a{v}^2$
• C. $\frac{v^2}{a}$
• D. $a{v}^2$

Answer 1

Answer: (B)

$2a{v}^2$

$y=a{x}^2\Rightarrow \frac{dy}{dt}=2ax\left(\frac{dx}{dt}\right)\Rightarrow \frac{dy}{dt}=2ax\left(v\right)\Rightarrow \frac{d^{2}y}{d{t}^2}=2av\left(\frac{dx}{dt}\right)\Rightarrow \frac{d^{2}y}{d{t}^2}=acceleration=2a{v}^2$