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A particle moves such that its position vector r(t) = cos ωt î + sin ωt ĵ where ω is a constant and t is time. Then which of the following statements is true for the velocity v(t) and acceleration a(t) of the particle:

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

Correct answer: v is perpendicular to r and a is directed towards the origin

Solution

The velocity vector v(t) is derived from the position vector r(t) and represents the tangent to the circular path, making it perpendicular to r. The acceleration vector a(t), which is centripetal in this case, points towards the center of the circular motion, thus directed towards the origin.

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