A body travels for `15 s` starting from rest with a constant acceleration. If it travels distances `x,y` and `z` in the first `5 s`, second 5 s and the next 5 s, repectively, the ralation between `x,y` and `z` is

Options

A. `x=y=z`
B. `5x=3y=z`
C. `x=y/3=z/5`
D. `x=y/5=z/3`

Answer

C

Explanation

`A` to `B: x=1/2a(5)^(2) …(i)`
`A` to `C: x+y=1/2a(5+5)^(2) …(ii)`
`A` to `D: x+y+z=1/2a(5+5+5)^(2) …(iii)`
Dividing (ii) by (i), we get
`(x+y)/x=4impliesy=3x`
Dividing (iii) by (ii), we get
`(x+y+z)/(x+y)=9/4`
`(4x+z)/(x+y)=9/4impliesz=5x`
`y=3x, z=5x`
`x=y/3=z/5`