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A particle moves so that its position vector is given by r̄ = cosωt î + sinωt ĵ. Where ω is a constant. Which of the following is true?

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

Correct answer: Velocity is perpendicular to r̄ and acceleration is directed towards the origin

Solution

The position vector describes circular motion. The velocity is tangential to the circle and hence perpendicular to the position vector. The acceleration, being centripetal, points towards the origin, which is the center of the circle.

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