Motion of a Powered Vehicle

Air resistance increases with speed. Top Speed is reached by vehicles when the driving force is equal to the air resistance.Initially drag is zero and a = ΣF/mDrag increases with speedSo at terminal speed F_R = F_E and acceleration is zeroThe engine provides a driving force F_E forwards. The resistive forces F_R (air resistance and friction) act backwards. By Newton's second law:F_E - F_R = maWhen the vehicle starts from rest, the resistive force is small, so the acceleration is large. As the speed increases, the air resistance increases, so the resultant force and the acceleration decrease. The vehicle reaches its top speed when F_R = F_E and the resultant force is zero.A vehicle's top speed can be increased by a larger driving force or by a more streamlined shape, which reduces air resistance at any given speed.When a vehicle tows a trailer, treat the vehicle and trailer as one object to find the acceleration. Then apply F = ma to the trailer alone to find the force in the tow bar or rope.