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  4. The velocity and acceleration of a point-like body at the initial moment of its motion are v0 =8 m s- 1 and a=2 m s- 2 respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-wm6gdvaoqq6m.png />

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Q. The velocity and acceleration of a point-like body at the initial moment of its motion are $v_{0 \, }=8 \, m \, s^{- 1}$ and $a=2 \, m \, s^{- 2}$ respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is

Question

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

The acceleration vector shall change the component of velocity uII along the acceleration vector.
$r=\frac{v^{2}}{a_{\text{n}}}$
The radius of curvature $r_{min }$ means v is minimum and an is maximum. This is at the point $P$ when the component of velocity parallel to the acceleration vector becomes zero, that is uII = 0.
Solution
$\therefore R=\frac{u_{\bot}^{2}}{a}=\frac{4^{2}}{2}=8\text{ m}$