1. Velocity and acceleration both are perpendicular to r . 2. Velocity and acceleration both are parallel to r . 3. Velocity is perpendicular to r and acceleration is directed towards the origin. 4. Velocity is perpendicular to r and acceleration is directed away from the origin.

Answer: 3. Velocity is perpendicular to r and acceleration is directed towards the origin. Key idea: this is uniform circular motion of unit radius. vec v=dotvec r=ω(-sinω t hat x+cosω t hat y) ; vec v·vec r=0 , so velocity is perpendicular to vec r . vec a=-ω²vec r , so acceleration points toward the origin.

Topic: Uniform circular motion· Kinematics

A particle moves so that its position vector is given by r = ω t x + ω t y. Where ω is a constant. Which of the following is true ?

1. Velocity and acceleration both are perpendicular to \(\vec{r}\).

2. Velocity and acceleration both are parallel to \(\vec{r}\).

3. Velocity is perpendicular to \(\vec{r}\) and acceleration is directed towards the origin.

4. Velocity is perpendicular to \(\vec{r}\) and acceleration is directed away from the origin.

Doubtly Asked 30 Oct 2026 NEET UG 2016 Phase 1 Practice test neet Save WhatsApp Report

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Answer: 3. Velocity is perpendicular to \(\vec{r}\) and acceleration is directed towards the origin.

Key idea: this is uniform circular motion of unit radius.

\(\vec v=\dot{\vec r}=\omega(-\sin\omega t\,\hat x+\cos\omega t\,\hat y)\); \(\vec v\cdot\vec r=0\), so velocity is perpendicular to \(\vec r\).
\(\vec a=-\omega^2\vec r\), so acceleration points toward the origin.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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A particle moves so that its position vector is given by r = ω t x + ω t y. Where ω is a constant. Which of the following is true ?

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