Final answer:
The speed of the water at point P in the syringe would be calculated using the cross-sectional areas of the syringe barrel and needle, along with the plunger's speed, applying the continuity equation A1V1 = A2V2.
Step-by-step explanation:
The question asks about the speed of the water at a specific point in a syringe. According to principles of fluid dynamics, specifically Bernoulli's principle and the conservation of mass (continuity equation), the speed at which water exits a narrowed section of a tube is considerably faster than when it is in the wider section. To find the exact speed, one would use the area of the barrel and the area of the needle, along with the volumetric flow rate or speed of the plunger, and apply the formula A1V1 = A2V2, where A represents the cross-sectional area and V represents the velocity at points 1 and 2. Given the dimensions of the barrel and needle and the plunger speed, the calculation would yield the flow rate in both the barrel and needle, and the resulting velocity of the liquid at point P.