To calculate the work done on a particle to accelerate it from rest to a speed of 0.081 c, we can use the equation for the kinetic energy of an object:
KE = (1/2)mv^2
Where KE is the kinetic energy, m is the mass of the particle, and v is its velocity.
Since the particle starts from rest, its initial kinetic energy is zero. The work done on the particle will be equal to the change in its kinetic energy.
ΔKE = KE_final - KE_initial
= (1/2)mv^2 - 0
ΔKE = (1/2)mv^2
So, the work done on the particle is equal to the change in kinetic energy, which is given by (1/2)mv^2.
Please note that "c" in the context of your question is commonly used to represent the speed of light, which is a constant. If you meant something else by "0.081 c," please clarify.