A) \[1:4:9\]
B) \[1:2:3\]
C) \[1:3:5\]
D) \[1:5:6\]
E) \[1:5:13\]
Correct Answer: C
Solution :
Distance covered in a particular time is \[{{s}_{n}}=u+\frac{1}{2}g(2n-1)\] \[\therefore \] \[{{s}_{1}}=0+\frac{1}{2}g(2\times 1-1)=\frac{g}{2}\] \[{{s}_{2}}=0+\frac{1}{2}g(2\times 2-1)=\frac{3}{2}g\] and \[{{s}_{3}}=0+\frac{1}{2}g(2\times 3-1)=\frac{5}{2}g\] Hence, the required ratio is \[{{s}_{1}}:{{s}_{2}}:{{s}_{3}}=\frac{g}{2}:\frac{3}{2}g:\frac{5}{2}g\] \[=1:3:5\]
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