19 A particle moves so that its acceleration, \(a \mathrm {~ms} ^ { - 2 }\), at time \(t\) seconds may be modelled in terms of its velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), as
$$a = - 0.1 v ^ { 2 }$$
The initial velocity of the particle is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)
19
- By first forming a suitable differential equation, show that
$$v = \frac { 20 } { 5 + 2 t }$$
19
- Find the acceleration of the particle when \(t = 5.5\)