5 The graph shows a model for the resultant horizontal force on a car, which varies as it accelerates from rest for 20 seconds. The mass of the car is 1200 kg .
\includegraphics[max width=\textwidth, alt={}, center]{c02cf013-365b-44e2-8c16-aa8209cbe250-4_373_1203_445_390}

1. The acceleration of the car at time \(t\) seconds is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Show that $$a = \frac { 2 } { 3 } + \frac { t } { 20 } , \text { for } 0 \leqslant t \leqslant 20$$
2. Find an expression for the velocity of the car at time \(t\).
3. Find the distance travelled by the car in the 20 seconds.
4. An alternative model assumes that the resultant force increases uniformly from 900 to 2100 newtons during the 20 seconds. Which term in your expression for the velocity would change as a result of this modification? Explain why.