1. A vehicle comprising: an engine; a braking system; and a controller configured to in response to a detected forward object and an adaptive cruise control mode being active, control the engine and braking system to decelerate the vehicle, and in response to a distance to the detected forward object falling below a first predefined threshold and a vehicle speed falling below a second predefined threshold with the adaptive cruise control mode being active, automatically control the braking system to apply a braking torque to brake the vehicle to a full stop and hold the vehicle stationary in an absence of powertrain torque based on a current road grade, and auto-stop the engine.