The magnitude of the force the motorcycle exerts backward on the ground to produce its acceleration of 3.50 m/s², considering its mass including the rider is 245 kg and the total resistive forces are 400 N, is 1257.5 N.
To find the magnitude of the force the motorcycle exerts backward on the ground to produce acceleration, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a).
The equation is often written as F = ma. Given that the mass of the motorcycle with rider is 245 kg and the acceleration provided is 3.50 m/s², we can calculate the force needed for this acceleration prior to accounting for resistive forces.
The formula would give us F = 245 kg * 3.50 m/s², resulting in a force of 857.5 N exerted for acceleration.
However, we must also overcome the resistive forces, which include friction and air resistance, totaling 400 N.
Therefore, the total force exerted backward on the ground by the motorcycle is the sum of the force needed for acceleration plus the force needed to overcome resistance: 857.5 N + 400 N = 1257.5 N.