A particle moving in the plane experiences a velocity dependent force

PHYSICS · Single correct · AP · Physics C: Mechanics · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A particle moving in the

xy

plane experiences a velocity dependent force

\vec{F} = k(v_y \hat{i} + v_x \hat{j})

, where

v_x

and

v_y

are

x

and

y

components of its velocity

\vec{v}

. If

\vec{a}

is the acceleration of the particle, then which of the following statements is true for the particle? (1) quantity

\vec{v} \times \vec{a}

is constant in time (2)

\vec{F}

arises due to a magnetic field (3) kinetic energy of particle is constant in time (4) quantity

\vec{v} \cdot \vec{a}

is constant in time