First, use the equation of motion:

\(v = u + at\)

where \(v = 4.5 \text{ m/s}\), \(u = 2.5 \text{ m/s}\), and \(t = 5 \text{ s}\).

Substitute the values:

\(4.5 = 2.5 + a \times 5\)

Solve for \(a\):

\(a = 0.4 \text{ m/s}^2\)

Next, apply Newton's second law:

\(F - 1.5 = 0.2a\)

Substitute \(a = 0.4\):

\(F - 1.5 = 0.2 \times 0.4\)

\(F - 1.5 = 0.08\)

Solve for \(F\):

\(F = 1.58 \text{ N}\)