Question

Is it possible for a particle to have negative kinetic energy in a barrier?

Answer 1

No never...Kinetic Energy can never be negaive...

As K.E =
$\frac{1}{2} m {v}^{2}$
Here m = mass of a particle...which is a scalar quantity and we dont have negative mass...

v = velocity of a particle , though velocity is a vector quantity so it can be negative...But we have square of velocity which makes velocity always positive....(square of any number whether a negative or positive always a positive)
So K.E cannot be negative...Atmost it can be zero only if velocity of a particle is zero or particle is at rest..