Question

Q) The position x of a particle at time t is given by x= vo/a (1-e-at) where vo is a constant and ao . The dimensional formula of vo and a are?

Answer 1

The position x of a particle at time t is given by $x=\frac{v_0}{a}(1-e^{-at})$ where $v_0$ is constant.

power of exponential must be dimensionless quantity.

so, -at is dimensionless quantity.

we know, dimension of t = [T]

so, for dimensionaless of -at , dimension of a should be [T^-1].

hence, dimension of a = [T^-1]

again, dimension of x = dimension of $v_0$/dimension of a

or, [L] = dimension of $v_0$/[T^-1]

or, dimension of $v_0$ = [LT^-1]

so, dimensional formula of $v_0$ is [LT^-1] and a is [T^-1]

Answer 2

Answer:

note : if a dimensionless quantity is given

then equate them to 1¹.

if it is useful mark it as brainliest answer and follow me for best answers