The acceleration of the particle is the derivative of the velocity function with respect to time. So, (a(t) = v'(t) = 6t - 2). At time (t = 2) seconds, the acceleration is (a(2) = 6(2) - 2 = 10) m/s^2.

The equation of motion for a mass-spring system is given by (mx'' + kx = 0), where (m) is the mass, (k) is the spring constant, and (x) is the displacement from the equilibrium position. In this case, (m = 10) kg, (k = 100) N/m, and the initial displacement is (x_0 = 0.05) m. So, the equation of motion is (10x'' + 100x = 0).

The rate of heat flow through the rod is given by the equation (Q = -kA\frac{dT}{dx}), where (k) is the thermal conductivity of the rod, (A) is the cross-sectional area of the rod, and (\frac{dT}{dx}) is the temperature gradient. In this case, (k = 200) W/(m K), (A = 0.01) m^2, and (\frac{dT}{dx} = -20) K/m. So, the rate of heat flow at (x = 2) meters is (Q = -200(0.01)(-20) = -40) W.

The equation of motion for a pendulum is given by (m\frac{d^2\theta}{dt^2} + mg\sin\theta = 0), where (m) is the mass of the pendulum bob, (g) is the acceleration due to gravity, (L) is the length of the pendulum, and (\theta) is the angle the pendulum makes with the vertical. This equation is a second-order nonlinear differential equation.

The equation of motion for the charge on the capacitor in an LRC circuit is given by (LC\frac{d^2q}{dt^2} + RC\frac{dq}{dt} + \frac{1}{C}q = 0). This equation is a second-order linear differential equation.