The velocity of a particle is at any time related to the distance travelled by the particle by the relation `v(x) = ax + b`, where `a` is positive and `b` is `le (a)/(b)`. Which of the following statement will be tue for this motion? (given `x = 0` where `t = 0`)

Options

A. The displacement of the particle at time t is `x = (b)/(a) (e^(at) -1)`
B. The particle will experience a retardation if `b lt 0`
C. The particle will be at rest at time `t = 0`
D. The motion of the particle is under constant acceleration

Answer

A, B

Explanation

`(dx)/(dt) = ax + b`
`int_(0)^(x) (dx)/((ax + b)) = int_(0)^(t) dt`
`{ln (ax + b)]_(0)^(x) = at`
`ln. ((ax + b))/(b) = at`
`x = (b)/(a) (e^(at) - 1)`