If a particle moves with position vector vec r (t), the velocity vector is tangent to the path. What is the acceleration vector's relation to the path?

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SSC Applied Mathematics QUESTION #4144

Question 1

If a particle moves with position vector $\vec{r}(t)$, the velocity vector is tangent to the path. What is the acceleration vector's relation to the path?

Always tangent to the path
Always normal to the path
Has both tangential and normal components✔️
Always perpendicular to velocity

Correct Answer Explanation

Acceleration $\vec{a} = \frac{dV}{dt}\hat{T} + \frac{V^2}{\rho}\hat{N}$, where $\hat{T}$ is unit tangent and $\hat{N}$ is unit normal. It has both tangential ($\frac{dV}{dt}$) and normal ($\frac{V^2}{\rho}$) components.

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