114 學年度臺灣大學轉學生招生考試｜第 54 題
普通物理學(A)
- 2.4 m/s
- 4.9 m/s
- 9.8 m/s
- 19.8 m/s
- 29.4 m/s
提示
With no friction, mechanical energy is conserved, so the final speed depends only on the net vertical drop from the start to the finish — not on the dips along the way.
正確答案
正解：D
詳解
A. (A) 2.4 m/s — incorrect. Far too small; this is not consistent with a 20 m drop.
B. (B) 4.9 m/s — incorrect. This is numerically g/2, a sign of plugging numbers into the wrong relation rather than v = √(2gΔh).
C. (C) 9.8 m/s — incorrect. This equals g; it is a units confusion, not a speed derived from energy conservation.
D. (D) 19.8 m/s — correct. The coaster starts at rest at the top and ends at the finish, which the figure marks as h = 20 m below the start line (the 25 m is just the depth of the intermediate valley and does not matter when there is no friction). Energy conservation: ½v² = gΔh, so v = √(2 × 9.8 × 20) = √392 ≈ 19.8 m/s.
E. (E) 29.4 m/s — incorrect. Too large; this would require a drop of about 44 m, larger than the actual net descent.
