Question

The displacement x of a particle varies with time t,x=ae−αt+beβt, where a,b,αand βare positive constants. The velocity of the particle will

Answer 1

I hope that its help u

Answer 2

Explanation :

Displacement of the particle is given as $x=ae^{-\alpha t}+be^{\beta t}$

Velocity is given by rate of change of displacement i.e.

$v=\dfrac{dx}{dt}$

$v=\dfrac{d}{dt}(ae^{-\alpha t}+be^{\beta t})$

$v=b\beta e^{\beta t}-a\alpha e^{-\alpha t}$

This is the expression for the velocity of the particle. Here $\alpha,\beta$ are constants.

Hence, this is the required solution.