Final answer:
The magnitude of the force that the motorcycle exerts backward on the ground to produce its acceleration, considering a mass of 245 kg and an acceleration of 3.50 m/s² while overcoming resistive forces of 400 N, is 1,257.5 N.
Step-by-step explanation:
To find the magnitude of the force that a motorcycle exerts backward on the ground to produce its acceleration, we'll use Newton's second law of motion, which states that the force is equal to mass times acceleration (F = ma). In this case, the total force exerted by the motorcycle also needs to overcome the forces resisting motion, such as friction and air resistance. Hence, the net force is the sum of the resistive forces and the force required to produce acceleration.
The mass of the motorcycle with the rider is 245 kg, and the acceleration provided is 3.50 m/s². We begin by calculating the force required for the acceleration:
- F = ma = 245 kg × 3.50 m/s² = 857.5 N
We then add the resistive forces to the calculated force:
- Total force exerted = force for acceleration + resistive forces = 857.5 N + 400 N = 1,257.5 N
Therefore, the magnitude of force the motorcycle exerts backward on the ground is 1,257.5 N.