To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ KJ. [The coefficient of friction between tyre of bus and road is 0.04.]

To maintain a constant speed, the bus has to overcome the frictional force acting on it. The frictional force is given by: <br/><br/> $F_{friction} = \mu F_N$ <br/><br/> Where $\mu$ is the coefficient of friction and $F_N$ is the normal force acting on the bus. Since the bus is on a flat road, the normal force is equal to the gravitational force: <br/><br/> $F_N = mg$ <br/><br/> Where $m$ is the mass of the bus and $g$ is the acceleration due to gravity (approximately $9.8 \mathrm{~m/s^2}$). <br/><br/> Substituting the values, we get: <br/><br/> $F_{friction} = 0.04 \times 500 \times 9.8$<br/><br/> $F_{friction} = 196 \mathrm{~N}$ <br/><br/> To maintain a constant speed, the engine must exert a force equal in magnitude to the frictional force. The work done by the engine to overcome the frictional force is given by: <br/><br/> $W = F_{friction} \times d$ <br/><br/> Where $d$ is the distance traveled. First, convert the distance from km to m: <br/><br/> $$d = 4 \mathrm{~km} \times \frac{1000 \mathrm{~m}}{1 \mathrm{~km}} = 4000 \mathrm{~m}$$ <br/><br/> Now, calculate the work done: <br/><br/> $W = 196 \mathrm{~N} \times 4000 \mathrm{~m}$ $W = 784000 \mathrm{~J}$ <br/><br/> Convert the work done from joules to kilojoules: <br/><br/> $W = \frac{784000 \mathrm{~J}}{1000 \mathrm{~J/ kJ}} = 784 \mathrm{~kJ}$ <br/><br/> The work done by the engine of the bus to maintain a speed of 80 km/h for a 4 km distance is $784.8 \mathrm{~kJ}$.