The trajectory of a particle moving in a plane is expressed in polar coordinates (r, θ) by the equations \(r=r_0 e^{β t} \text { and } \frac{d \theta}{d t}=ω\), where the parameters r0, β and ω are positive. Let vr and ar denote the velocity and acceleration, respectively, in the radial direction. For this trajectory
1
ar < 0 at all times irrespective of the values of the parameters
2
ar > 0 at all times irrespective of the values of the parameters
3
\(\frac{d v_r}{d t}>0\) and ar > 0 for all choices of parameters
4
\(\frac{d v_r}{d t}>0\) however, ar = 0 for some choices of parameters