Final answer:
The magnitude of the force that a motorcycle with a rider mass of 245 kg exerting a 3.50 m/s² acceleration exerts backward on the ground to overcome resistance and accelerate is calculated using Newton's second law. The total force, considering the resistance of 400 N, is 1257.5 N.
Step-by-step explanation:
To calculate the magnitude of the force a motorcycle exerts backward on the ground to produce its acceleration, we use Newton's second law, which states that force equals mass times acceleration (F=ma). The motorcycle with a rider has a mass of 245 kg and an acceleration of 3.50 m/s².
Additionally, we know that the motorcycle needs to overcome a total resistance force of 400 N due to friction and air resistance.
The net force exerted by the motorcycle is the force necessary to accelerate the motorcycle at 3.50 m/s² plus the force to overcome the resistance. Mathematically, the net force can be expressed as:
Net Force = Mass × Acceleration
Net Force = 245 kg × 3.50 m/s²
Net Force = 857.5 N
However, to find the total force exerted by the motorcycle backward on the ground, we must add the resistance force:
Total Force = Net Force + Resistance Force
Total Force = 857.5 N + 400 N
Total Force = 1257.5 N
Therefore, the total force the motorcycle exerts backward on the ground to produce its acceleration, while overcoming the resistance forces, is 1257.5 N.