question_answer

The driver of a train moving with a constant speed \[{{\text{v}}_{1}}\] along a straight track sights another train at a distance d ahead of him on the same track moving in the same direction with a constant speed \[{{\text{v}}_{2}}\] He at once applies the brakes and gives his train a constant retardation f. There will be a collision of the trains if

A) \[{{\text{v}}_{1}}>{{\text{v}}_{2}}\,\,\,and\,\,\,\frac{{{({{\text{v}}_{1}}-{{\text{v}}_{2}})}^{2}}}{2f}<d\]

B) \[{{\text{v}}_{1}}<{{\text{v}}_{2}}\,\,\,and\,\,\,\frac{{{({{\text{v}}_{1}}+{{\text{v}}_{2}})}^{2}}}{2f}>d\]

C) \[{{\text{v}}_{1}}>{{\text{v}}_{2}}\,\,\,and\,\,\,\frac{{{({{v}_{1}}-{{\text{v}}_{2}})}^{2}}}{2f}>d\]

D) \[{{\text{v}}_{1}}>{{\text{v}}_{2}}\,\,\,and\,\,\,\frac{(\text{v}_{1}^{2}-\text{v}_{2}^{2})}{2f}>d\]