Final answer:
To calculate the force exerted backward by a motorcycle on the ground to produce acceleration, one must consider both the mass-acceleration product and the resistance forces. The force is calculated using Newton's second law, resulting in a total force of 1257.5 Newtons, after accounting for both the net force required to produce the acceleration and the resistance forces.
Step-by-step explanation:
To find the magnitude of the force the motorcycle exerts backward on the ground to produce its acceleration, we can use Newton's second law of motion. This law states that force equals mass times acceleration (F = ma). Given that the mass of the motorcycle with rider is 245 kg and the acceleration is 3.50 m/s², we can calculate the net force required to produce this acceleration. However, we must also take into account the 400 N force of friction and air resistance opposing the motion.
First, we calculate the net force required for acceleration without resistance: F_net = mass × acceleration = 245 kg × 3.50 m/s² = 857.5 N. Next, we add the force of resistance to the net force to find the total force exerted by the motorcycle: F_total = F_net + resistance = 857.5 N + 400 N = 1257.5 N. Therefore, the total force that the motorcycle exerts backward on the ground to produce its acceleration is 1257.5 Newtons.