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

Options

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

Answer

A

Explanation

Here `at` is dimensionless. So
` a = (1)/( t) = [(1)/(T)] = [T^(-1)] x = (V_(0))/(a) and V_(0) = xa = [ LT^(-1)]`
` = [M^(0)LT^(-1)]`