A car of mass $600{\text{ }}kg$ travels along a straight horizontal road starting from a point $A$. The resistance to motion of the car is $750{\text{ }}N$.
a) The car travels from $A$ to $B$ at constant speed in $100{\text{ }}s$. The power supplied by the car’s engine is constant and equal to $30{\text{ }}kW$. Find the distance $AB$.
b) The car’s engine is switched off at $B$ and the car’s speed decreases until the car reaches $C$ with a speed of $20{\text{ }}m{\text{ }}{s^{ - 1}}$. Find the distance $BC$.
c) The car’s engine is switched on at $C$ and the power it supplies is constant and equal to $30{\text{ }}kW$. The car takes $14{\text{ }}s$ to travel from $C$ to $D$ and reaches $D$ with a speed of $30{\text{ }}m{\text{ }}{s^{ - 1}}$. Find the distance $CD$.
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