Using the formula for power, \(P = Fv\), where \(F\) is the force exerted by the engine, we have:

\(\frac{P}{v} - R = ma\)

For \(v = 19\) m/s and \(a = 0.6\) m/s\(^{-2}\):

\(\frac{P}{19} - R = 1250 \times 0.6\)

For \(v = 30\) m/s and \(a = 0.16\) m/s\(^{-2}\):

\(\frac{P}{30} - R = 1250 \times 0.16\)

We have two equations:

1. \(\frac{P}{19} - R = 750\)
2. \(\frac{P}{30} - R = 200\)

To eliminate \(R\), subtract the second equation from the first:

\(\frac{P}{19} - \frac{P}{30} = 750 - 200\)

\(\frac{30P - 19P}{570} = 550\)

\(11P = 550 \times 570\)

\(P = 28500\)

Substitute \(P = 28500\) back into the first equation:

\(\frac{28500}{19} - R = 750\)

\(1500 - R = 750\)

\(R = 750\)