A body travels 200 cm in the first two seconds and 220 cm in the next 4 seconds with deceleration. the velocity of the body at the end of the `7^(th)` second is

Options

A. `10 " cm s"^(-1)`
B. `20 " cm s"^(-1)`
C. `5 " cm s"^(-1)`
D. `30 " cm s"^(-1)`

Answer

A

Explanation

Let u and a be the initial velocity and uniform acceleration of the body.

Using, `S=ut + 1/2, " " :. 200 = u(2)+1/2 a(2)^(2) `
or ` 100 = u +a" "...(i)`
and `420 = 6u +1/2 a(6)^(2), " or " 70 = u +3a " "...(ii)`
Solving equations (i) and (ii) , we get
`u=115 "cm " s^(-1), a = - 15 "cm "s^(-1)`
Using , v = u + at
`:. v = 115 + (-15)7 = 10 "cm "s^(-1)`