The motive force produced by the engine is not constant because of limitations in the mechanical design of engines. Each time a car goes up a gear, it trades some of the motive force for allowable speed such that the product of force and speed (power) is maintained under the mechanical limits of the engine.
The higher the speed of the car, the longer the gear ratio needed to maintain the engine speed its limits. The longer the gear ratio is, the less torque multiplication happens through the drive train and less torque arrives at the wheels.
After torque is converted into motive force by the tires and the contact patch, you must also include other forces that apply to the car to get to use $F = m a$. Other forces include some portion of the weight of the car if the car is moving up a grade, aerodynamic resistance when the car is moving at higher speeds, rolling resistance of the tires, friction, and engine compression as well as other mechanical losses through the drivetrain.
Broadly speaking, considering the motive force of the engine and the air drag is sufficient to apply Newton's law of motion
$$ F_{\rm engine} - F_{\rm drag} = m_{\rm car} a_{\rm car} $$
and if the car is going up a grade of $\theta$ degrees
$$ F_{\rm engine} - F_{\rm drag} = m_{\rm car} ( a_{\rm car} + g \sin \theta) $$
Very broadly you can modeestimate the motive force of the engine from the power it produces at any moment
$$ F_{\rm engine} = \frac{P_{\rm engine}}{v_{\rm car}} $$
and the aerodynamic force that increases parabolically with speed
$$ F_{\rm drag} = \beta \; v_{\rm car}^2 $$