A compact front$-$wheel$-$drive car has a mass of $720$ kg and a wheelbase of $2\mathrm{.}04$ m$.$ The centre of mass is $0\mathrm{.}775$ m behind the front axle and $0\mathrm{.}650$ m above the ground. The vehicle has an effective frontal area of $1\mathrm{.}5$ m$?$ and an aerodynamic drag coefficient of $0\mathrm{.}29.$ The mass density of air can be assumed to be $1\mathrm{.}23$ kg$/$m$\backslash$deg $.$ The coefficient of rolling resistance of thetires is $0\mathrm{.}014$ and the rolling radius of the tires is $0\mathrm{.}30$ m$.$ The coefficient of road adhesion is $0\mathrm{.}8.$The vehicle is equipped with an automatic transmission consisting of a torque converter and a $4-$speed gearbox $($including one overdrive gear$).$ The engine characteristics and torque converter characteristics are provided in Figures $1$ and $2$ respectively. The gear ratio of the drive axle is $3\mathrm{.}94$ and that of the third gear in the gearbox is $1\mathrm{.}03.$ The combined driveline efficiency $($excluding that of the torque converter$)$ is $0\mathrm{.}91.$The vehicle is towing a trailer having a mass of $300$ kg up a $10\%$ grade. The rolling resistance coefficient of the tires for the trailer is the same as that for the vehicle. The frontal area of the trailer is smaller than that of the vehicle and, as a first approximation, its aerodynamic resistance may be neglected. The mass factor Ym for the car is given byYm $=1\mathrm{.}04+0\mathrm{.}002552$where So is the overall gear reduction ratio $($excluding any effect due to the torque converter$)$; for the trailer, Ym may be taken to be $1\mathrm{.}02\mathrm{.}1.$ Determine the acceleration of the vehicle$-$trailer combination on the $10\%$ slope with a headwind of $15$ km$/$h when the engine operates at $2000$ rpm with wide$-$open throttle and with the third gear in the automatic gearbox engaged. It may be assumed that the surface conditions are such that the vehicle is operating with low longitudinal slip of $3\%.$ It also may be assumed that the trailer does not affect the vertical loading on the car's wheels$\mathrm{.}2.$ Determine the instantaneous fuel consumption corresponding to this operating condition and express it in units of kg$/$kW$-$hr$.$

Figure $1$: Engine characteristic for use in Question $1.$