To maintain a speed of 80km h ^ - 1 by a bus of mass 500kg on a...

It is given,

$v = 80km{h}^{- 1}$

$m = 500kg$

$S = 4km$

$\mu = 0 . 04$

The power due to friction is

${P}_{f} = Fv$ where $F = \mumg$

$= \left(\left(0 . 04\right)\left(500 \times 9 . 8\right) \times 80 \times \dfrac{5}{18}\right)W$

Hence, the work done by the engine in overcoming the friction is

$W = {P}_{f}t = {P}_{f}\dfrac{d}{v}$

$⇒ W = 20 \times 9 . 8 \times 80 \times \dfrac{5}{18} \times \dfrac{4 \times {10}^{3}}{80 \times \dfrac{5}{18}} = 784kJ$