A) \[3\text{ }m{{s}^{-1}}\]
B) \[2.5\text{ }m{{s}^{-1}}\]
C) \[2\text{ }m{{s}^{-1}}\]
D) \[\text{1 }m{{s}^{-1}}\]
Correct Answer: D
Solution :
Let u be the initial velocity that have to find and a be the uniform acceleration of the particle. For \[t=3s\], distance travelled \[S=12\text{ }m\]and For \[t=3+3=6\text{ }s\] distance travelled \[S=12+30=42\text{ }m\] From, \[S=ut\text{ }+\text{ }1/2\text{ }a{{t}^{2}}\] \[12=u\times 3+\frac{1}{2}\times a\times {{3}^{2}}\] Or \[24=6y+9a~~~~~~~~~~~~~~~...\left( i \right)\] Similarly, \[42=u\times 6+\frac{1}{2}\times a\times {{6}^{2}}\] Or \[42=6y+18a~~~~~~~~~~~~~~~~~~...\left( ii \right)\] On solving, we get \[u=1\text{ }m\text{ }{{s}^{-1}}\]
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