Trên một tuyến đường xe buýt thẳng, các xe buýt chuyển động theo một chiều và cách đều nhau 5 km. Một người đi xe đạp chuyển động thẳng đều trên tuyến đường này. Nếu đi theo một chiều thì tại thời điểm t = 0, người đi xe đạp gặp xe buýt thứ nhất, đến thời điểm t = 1h, người này gặp xe buýt thứ 12. Nếu đi theo chiều ngược lại thì thời điểm t = 0, người đi xe đạp gặp xe buýt thứ nhất, đến thời điểm t = 1 h người này gặp xe buýt thứ 6. Hỏi nếu người này đứng yên bên đường thì trong 1 giờ tính từ thời điểm gặp xe buýt thứ nhất, người này còn gặp được bao nhiêu xe buýt nữa? Bỏ qua kích thước của xe buýt và xe đạp.
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* Trường hợp 1: Xe đạp và xe buýt đi cùng chiều.
Trong 1 giờ, xe đạp gặp 11 xe buýt. Quãng đường xe đạp đi được nhiều hơn quãng đường 11 xe buýt đi là $11 \times 5 = 55$ km.
$v_1 - v_2 = 55$ (1)
* Trường hợp 2: Xe đạp và xe buýt đi ngược chiều.
Trong 1 giờ, xe đạp gặp 5 xe buýt. Quãng đường xe đạp đi được cộng quãng đường 5 xe buýt đi là $5 \times 5 = 25$ km.
$v_1 + v_2 = 25$ (2)
Từ (1) và (2), ta có: $2v_2 = 25-55=-30$. Suy ra $v_2=-15$ km/h (vận tốc âm do chọn chiều dương là chiều xe đạp đi).
Vậy nếu người đứng yên thì trong 1 giờ, số xe buýt người đó gặp là $|v_2|/5 = 15/5 = 3$ xe.
Nhưng vì người đó đã gặp xe buýt đầu tiên nên số xe buýt gặp thêm là $2v_2/5 +1= 3-(-15) +1 = 3 + 6= 9$ xe.
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