During exercise or a lot of activity we know that heart rate increases. Sympathetic neurons also stimulate arteries and veins to change shape. My question is which arteries and veins dilate and which constrict? During exercise do arteries leading to muscles dilate so that more blood volume reaches them? But of they dilate won't speed decrease?

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I think that arteries should neither constrict nor dilate since by dilating volume increases but speed decreases and on constricting speed increases and volume decreases. This is according to the Physics Equation: A1V1 = A2V2 where A is area and V is velocity.

Actually, they do dilate. Another factor which comes in is that the heart will pump more, faster. This results in an increase in pressure and an increase in the volume of blood entering the vein/artery.

Also, veins don't really dilate/constrict. They dilate/constrict depending on the pressure of the blood. They can dilate and become surprisingly large if the pressure is high (much bigger than a thumb ;) ). It's just like when the blood pressure is high, the blood will push on the vein to make it larger.