Final answer:
The magnitude of the force that a motorcycle exerts backward on the ground to produce an acceleration of 3.50 m/s² with a mass of 245 kg and resisting forces of 400 N is 1257.5 N.
Step-by-step explanation:
To calculate the magnitude of the force the motorcycle exerts backward on the ground to produce its acceleration when traveling at 90.0 km/h, we'll use Newton's second law of motion, F = ma, where F is the net force acting on an object, m is the mass of the object, and a is its acceleration. Given that the mass of the motorcycle with the rider is 245 kg and the acceleration is 3.50 m/s², the force due to acceleration can be calculated as:
F = m × a = 245 kg × 3.50 m/s² = 857.5 N
Additionally, we must overcome the resistive forces (including friction and air resistance) totaling 400 N. To find the total force exerted by the motorcycle, we add this resistive force:
Total force = Force due to acceleration + Resistive force = 857.5 N + 400 N = 1257.5 N
Therefore, the motorcycle exerts a backward force of 1257.5 N on the ground to achieve the specified acceleration.