A street car moves rectilinearly from station A to the next station B (from rest to rest) with an acceleration varying according to the law `f = a-bx,` where a and b are constants and x is the distance from station A. The distance between the two stations and the maximum velocity are

Options

A. `(2a)/(b)`
B. `(a)/(b)`
C. `(a)/(2b)`
D. `2a - b`

Answer

A

Explanation

Acc. `= (a - bx)`
`v (dv)/(dx) = a - bx`
`int v dv = int (a - bx) dx`
`(v^(2))/(2) = ax - (bx^(2))/(2)`
`v^(2) = 2 ax - bx^(2)`
When `v = 0`,
`0 = 2 ax - bx^(2)`
`x = (2a)/(b)`