When the average kinetic energy of the molecules goes up (a rise in temperature), the average speed of the molecules increases. And lower average kinetic energy of the molecules means they have lower speed. However, a change in average kinetic energy is not directly proportional to a change in average speed. 1.
An appreciation means an increase in the value of a currency. It means a currency is worth more in terms of foreign currency.
In economics, finance, investing, and business in general, the terms appreciate and appreciation mean increasing value, almost always referring to the value of an asset. 1  A company can properly say that its real estate holdings (assets) are appreciating..