A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 s and a distance of 30 m in next 3 s. The initial velocity of the particle is

Options

A. `1 ms ^(-1)`
B. `2.5 ms ^(-1)`
C. `2 ms ^(-1)`
D. `15 ms ^(-1)`

Explanation

Given,
`s_(1) = 12 , t _(1) = 3s `
`s _(2) = 30 + 12 = 42 m`
`t _(2) = 3 +3 = 6s `
`because s = ut + (1)/(2) at ^(2)`
`therefore s _(1) = ut _(1) +(1)/(2) at _(1) ^(2)`
`12 = 3 xx u + (1)/(2) a xx 3 ^(2)`
`12 = 3u + (9)/(2) a " "...(i)`
Similarly, ` u ^(2) = 6u + (1)/(2) a 36 " "...(ii)`
Solving the Eqs. (i) and (ii), we get
`a =2 m//s ^(2),`
`u =1 m//s`
u is initial velocity.