Transverse component of velocity of a particle moving along a straight line in a plane:

We know that when a particle is moving along a curve in a plane, then the transverse component of velocity is \( {v}_{\theta}=r\dot{\theta} \).

[To know the derivation of the transverse component of velocity (CLICK HERE) ]

Since, here the particle is moving in the plane along a straight line, therefore the co-ordinate \( {\theta} \) remains unchanged, i.e., constant, only the co-ordinate \( r \) varies.

Now, \( \displaystyle{\frac{d\theta}{dt}}=\dot{\theta}=0 \), since \( \theta=constant \).

So the transverse component of the velocity is \( v_{\theta}=0 \)