Final answer:
The question involves calculating volumes and velocities related to pistons moving in cylinders, and determining uncertainties in measurements, which fall under the domain of High School level Physics.
Step-by-step explanation:
The question primarily deals with the principles of fluid mechanics in Physics, specifically with the concept of Pascal's principle, fluid dynamics, and hydraulic systems as applied to movements of pistons within cylinders containing water or gas. Determining the velocity of water leaving a spout and the change in gas volume due to piston movement involves using principles from Physics such as conservation of energy and the equation of continuity.
For the piston with a cross-sectional area of 0.07 m2, the change in volume due to piston movement would be calculated by multiplying this area by the distance the piston travels. To calculate potential uncertainties in volume (in the case of the car engine piston problem), error propagation techniques are used to find the combined uncertainty from the diameter and travel distance measurements.
In the case of the squirt toy example, Bernoulli’s principle and equations relating force, pressure, and area can be used to calculate the speed at which the water emerges from the toy.