A woman walks in a straight line. The woman’s velocity $t$ seconds after passing through a fixed point $A$ on the line is $vm{\text{ }}{s^{ - 1}}$. The graph of $v$ against $t$ consists of 4 straight line segments (see diagram). The woman is at the point $B$ when $t = 60$. Find
a) the woman’s acceleration for ${\text{0}} \lt {\text{t}} \lt {\text{30}}$ and for ${\text{30}} \lt {\text{t}} \lt {\text{40}}$,
b) the distance $AB$,
c) the total distance walked by the woman.

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