Final answer:
To determine if the motorcyclist will emerge from the sandy stretch without having to start the engine, calculate the frictional force and compare it to the product of the mass of the motorcycle and its acceleration.
Step-by-step explanation:
In order to determine if the motorcyclist will emerge from the sandy stretch without having to start the engine, we need to calculate the frictional force acting on the motorcycle. The frictional force can be calculated using the equation:
Ff = μN
where Ff is the frictional force, μ is the coefficient of kinetic friction, and N is the normal force. Since the motorcycle is coasting, the normal force is equal to the weight of the motorcycle, which can be calculated using the equation:
N = mg
where m is the mass of the motorcycle and g is the acceleration due to gravity. Plugging in the given values for the mass and the coefficient of kinetic friction, we can calculate the frictional force:
Ff = (0.65)(200 kg)(9.8 m/s2)
After calculating the frictional force, we can determine if it is enough to stop the motorcycle within the 14 m stretch of sand. If the frictional force is greater than or equal to the product of the mass of the motorcycle and its acceleration, then the motorcycle will stop within the sandy stretch and the engine will need to be started. If the frictional force is less than the product of the mass and acceleration, then the motorcycle will continue to coast through the sandy stretch and the engine will not need to be started. Compare the calculated frictional force with the product of the mass of the motorcycle and its acceleration to determine if the motorcycle will emerge from the sandy stretch without having to start the engine.