Một tàu hỏa dừng lại hẳn sau 30 s kể từ lúc bắt đầu hãm phanh. Trong thời gian đó tàu chạy được 180 m. Tính vận tốc của tàu lúc bắt đầu hãm phanh và gia tốc của tàu?
Một tàu hỏa dừng lại hẳn sau 30 s kể từ lúc bắt đầu hãm phanh. Trong thời gian đó tàu chạy được 180 m. Tính vận tốc của tàu lúc bắt đầu hãm phanh và gia tốc của tàu?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
- $v = v_0 + at$
- $x = x_0 + v_0t + \frac{1}{2}at^2$
Chọn $x_0 = 0$. Khi tàu dừng hẳn, $v = 0$. Ta có:
$0 = v_0 + 30a$ (1)
$180 = v_0(30) + \frac{1}{2}a(30)^2$ (2)
Từ (1), ta có $v_0 = -30a$. Thay vào (2), ta được:
$180 = -30a(30) + \frac{1}{2}a(30)^2$
$180 = -900a + 450a$
$180 = -450a$
$a = \frac{180}{-450} = -0.4$ m/s$^2$
Suy ra $v_0 = -30(-0.4) = 12$ m/s.
Vậy vận tốc ban đầu là 12 m/s và gia tốc là -0.4 m/s$^2$.
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