Final answer:
The magnitude of the force that the motorcycle exerts backward on the ground to produce an acceleration of 3.50 m/s², while overcoming a total resisting force of 400 N and having a mass of 245 kg with the rider, is 1257.5 N.
Step-by-step explanation:
To find the magnitude of the force that the motorcycle exerts backward on the ground, we use Newton's second law of motion which states that the force is equal to the mass times the acceleration (F = m * a). Here, the mass (m) is 245 kg and the acceleration (a) is 3.50 m/s². Additionally, we must account for the forces resisting motion, which total to 400 N.
The total force exerted by the motorcycle is the sum of the force needed to overcome resistance and the force needed to produce acceleration. Thus, the force to just overcome resistance is 400 N (since it already acts in the opposite direction) and the force for acceleration is the product of mass and acceleration.
Calculation:
Force for acceleration (Fa) = m * a = 245 kg * 3.50 m/s² = 857.5 N
Total force exerted by motorcycle (Ftotal) = Fa + force to overcome resistance = 857.5 N + 400 N = 1257.5 N
So, the magnitude of the force the motorcycle exerts backward on the ground is 1257.5 N.