Final answer:
The magnitude of the force the motorcycle exerts backward on the ground is calculated by adding the net force required for acceleration (245 kg × 3.50 m/s² = 857.5 N) to the resistive forces (400 N), resulting in a total force of 1257.5 N. The given answer choices do not match this calculation.
Step-by-step explanation:
To calculate the total 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 multiplied by the acceleration (F = m × a). In this case, the motorcycle has a mass of 245 kg and is undergoing an acceleration of 3.50 m/s². However, we must also consider the forces resisting motion (friction and air resistance) which total 400 N and act in the opposite direction to the force exerted by the motorcycle.
Therefore, the net force accelerating the motorcycle is the force exerted minus the resistive forces (Fnet = F - Fresistance). We know that:
Fnet = m × a = 245 kg × 3.50 m/s² = 857.5 N
To find the total force exerted by the motorcycle, we need to add the resistive forces:
F = Fnet + Fresistance = 857.5 N + 400 N = 1257.5 N
The magnitude of the force the motorcycle exerts backward on the ground is approximately 1257.5 N. There seems to be a discrepancy in the provided answer choices, as none of them match the calculated result. The provided answer may be based on a different mass, acceleration, or resistance value not included in the question text.