Question

A particle moves along the trajectory of parabola y = ax². Assuming speed to be constant, find the radius of curvature.

• A. 1/2a
• B. 1/a
• C. 1/2ax
• D. 2/a

Answer 1

Answer: (A)

1/2a

Answer 2

y = ax²; dy/dt = 2ax (dy/dt) or

$\frac{d^{2}y}{dt^{2}} = 2a\left( \frac{dx}{dt} \right)^{2} + 2ax\frac{d^{2}x}{dt^{2}}$

As the speed is constant only acceleration present is

a_r = $\frac{v^{2}}{r};\left. \ \frac{d^{2}y}{dt^{2}} \right|_{x = 0} = 2a\left( \frac{dx}{dt} \right)^{2}$

2av² = $\frac{v^{2}}{r}$ or R= $\frac{1}{2a}$.