(a) Apply Newton's second law to block B:

\(T - 40g \sin 20^{\circ} - 50 = 40a\)

Solving gives:

\(T = 40a + 136.8\)

Apply Newton's second law to block A:

\(500 \cos 15^{\circ} - 80g \sin 20^{\circ} - T = 80a\)

Substitute for \(T\):

\(500 \cos 15^{\circ} - 80g \sin 20^{\circ} - (40a + 136.8) = 80a\)

Simplify and solve for \(a\):

\(482.96 - 273.61 - 136.8 = 120a\)

\(a = 0.188 \text{ m/s}^2\)

Substitute \(a\) back to find \(T\):

\(T = 40(0.188) + 136.8 = 194 \text{ N}\)

(b) Use the equation \(v = u + at\) with \(u = 0\), \(v = 1.2 \text{ m/s}\), and \(a = 0.188 \text{ m/s}^2\):

\(1.2 = 0 + 0.188t\)

Solve for \(t\):

\(t = \frac{1.2}{0.188} = 6.39 \text{ s}\)