(i(a))[2]
The diagram gives an approximate velocity-time graph for the tractor's motion. It is formed from two straight-line sections. Use the graph to estimate the distance $AB$.
(i(b))[2]
Calculate the tractor's acceleration for $0 \le t \le 400$ and for $400 \le t \le 800$.
(ii(a))[3]
The tractor's actual velocity is given by $v = 0.04t - 0.00005t^{2}$ for $0 \le t \le 800$. Determine the values of $t$ for which the tractor's actual acceleration agrees with the approximate velocity-time graph from part (i).
(ii(b))[2]
For $0 \le t \le 400$, let the approximate tractor velocity from part (i) be $v_1\,\text{m s}^{-1}$. Write $v_1$ as a function of $t$ and hence show that $v_1 - v = 0.00005(t - 200)^2 - 1$.
(ii(c))[2]
Conclude that $-1 \le v_1 - v \le 1$.