A) \[\text{3}.\text{125 m}/{{\text{s}}^{\text{2}}}\]
B) \[\text{3}.\text{5 m}/{{\text{s}}^{\text{2}}}\]
C) \[\text{2}.\text{75 m}/{{\text{s}}^{\text{2}}}\]
D) \[\text{3}.0\text{ m}/{{\text{s}}^{\text{2}}}\]
Correct Answer: A
Solution :
Relative velocity of faster train with respect to slow train \[u=115-25=90\,\,km/hr\] \[=90\times \frac{5}{8}=~25\,\,m/\sec \] Distance between the two trains, \[s=100\,\,m\] Since in order to avoid collision, the relative velocity should be zero, therefore \[{{v}_{2}}={{u}_{2}}+2as\] \[\Rightarrow \] \[0-{{(25)}^{2}}=2\times a\times 100\] \[\Rightarrow \] \[-625=200\,\,a\] \[\Rightarrow \] \[a=-\frac{625}{200}=-3.125\,\,m/{{s}^{2}}\][\[-ve\] sign means retardation]
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