〔第40問〕
次の英文中の空欄（ア）から（オ）までに後記ａからｅまでの【数式】を入れる場合，その
組み合わせとして最も適切なものを，後記１から５までの中から選びなさい。（解答欄は，［?・
40］）
Physical phenomena can be described with a differentiation formula and with an
integration formula. The relation between the two expressions helps to clarify the
behavior. For example, by integrating twice the equation of motion when a body falls
downward, we can show that the law of mechanical conservation of energy is valid.
When the body starts to fall, the position and the velocity at the time t = 0 are y0 and υ0,
respectively. After the body has fallen, the position and the velocity at time t are y and υ,
respectively. The body has mass m. We do not consider air resistance. The acceleration of
the gravity is g.
Remember Newton’s second law of motion. The equation of motion, a second order
differential equation, is （ア）．
By dividing （ア） by m and integrating it, we obtain （イ）, where dy
dt means υ along
y direction at t. In （イ）, we substituted υ = υ0 when t = 0. Using （イ）, υ can be solved
as a function of t. By integrating the first order differential equation （イ）, it becomes
（ウ）, where y = y0 when t = 0. Using （ウ）, y can be solved as a function of t. By combining
（イ） and （ウ） with eliminating t, they can be written as （エ）.
This is the well-known law of mechanical conservation of energy. By transposition of
two terms in （エ）, we obtain （オ）.
In （オ）, it is clear that the decreasing of the potential energy is equal to the increasing
of the kinetic energy.
