A particle moves so that its position vector is given by r→=cosωt x^+sinωt y^, where ω is a constant.
Which of the following is true?
Velocity is perpendicular to r→ and acceleration is directed towards the origin.
Velocity is perpendicular to r→and acceleration is directed away from the origin
Velocity and acceleration both are perpendicular to r→
Velocity and acceleration both are parallel tor→
Given, r→=cosωt x^+sinωt y^
∴v→=dr→dt=-ωsinωt x^+ωcosωt y^
a→=dv→dt=-ω2cosωt x^-ω2sinωt y^=-ω2r→
Since position vector (r→) is directed away from the origin, so,
acceleration -ω2r→ is directed towards the origin.