For a particle moving along the ellipse dfrac x^2 a^2 +dfrac y^2 b^2 =1 with uniform speed V at the point (0,b), the tangential component of acceleration is:

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SSC Applied Mathematics QUESTION #1296

Question 1

For a particle moving along the ellipse \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\) with uniform speed \(V\) at the point \((0,b)\), the tangential component of acceleration is:

Zero✔️
\(\dfrac{V^2}{a}\)
\(\dfrac{V^2}{b}\)
\(\dfrac{V^2 b}{a^2}\)

Correct Answer Explanation

Uniform speed means \(|\vec{v}|=V=\text{constant}\), so \(\dfrac{d|\vec{v}|}{dt}=0\). The tangential component of acceleration \(a_T=\dfrac{dV}{dt}=0\). Only the normal (centripetal) component is non-zero.

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