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

Answer

`[v_(0)]=[m^(0)L^(1)T^(-1)][alpha]=[m^(0)L^(0)T^(-1)]`

Explanation

Dimension of `alpha t= M^(0)L^(0)T^(0)`
`rArr` Dimension of `alpha=M^(0)L^(0)T^(-1)`
Dimension of `v_(0)/alpha=L^(-1)`
`rArr` Dimension of `v_(0)=M^(0)L^(1)T^(-1)`