The position of a particle at time `t` is given by the relation `x (t) = (v_(0))/(A) (1 - e^(-At))`, where `v_(0)` is constant and `A gt 0`. The dimensions of `v_(0)` and `A` respectively

Options

A. `[M^(0)LT^(-1)]" and "[T^(-1)]`
B. `[M^(0)LT^(0)]" and "[T^(-1)]`
C. `[M^(0)LT^(-1)]" and "[LT^(-2)]`
D. `[M^(0)LT^(-1)]" and "[T]`

Answer

A

Explanation

`x=(v_0)/(a)(1-e^(-at))`
`at to` constant
`implies a[T] to k`
`implies a= [T^(-1)]`
x is the position
`[L]=(v_0)/([T^(-1)])`
`v_(0)= [M^(0)LT^(-1)]`