8 A particle of mass 4 kg moves horizontally in a straight line.
At time \(t\) seconds the velocity of the particle is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
The following horizontal forces act on the particle:
- a constant driving force of magnitude 1.8 newtons
- another driving force of magnitude \(30 \sqrt { t }\) newtons
- a resistive force of magnitude \(0.08 v ^ { 2 }\) newtons
When \(t = 70 , v = 54\)
Use Euler's method with a step length of 0.5 to estimate the velocity of the particle after 71 seconds.
Give your answer to four significant figures.