The work done by the external agent in moving the particle from surface a to surface b is 0.172 J.
To calculate the work done by the external agent in moving the particle from surface a to surface b, we need to find the change in kinetic energy of the particle. We can use the equation:
Work done = ΔKE = KEb - KEa
Where KE is the kinetic energy of the particle. The kinetic energy can be calculated using the equation:
KE = 0.5 * mass * speed2
Substituting the given values, we can calculate the work:
KEa = 0.5 × 3.45e-2 × (2.00)2 = 0.138 J
KEb = 0.5 × 3.45e-2 × (3.00)2 = 0.310 J
Work done = ΔKE = 0.310 J - 0.138 J = 0.172 J