The displacement x of a particle at time t

Asked by admin @ 23/08/2021 in Physics viewed by 285 People

The displacement x of a particle at time t along a straight line is given by x = α -βt +γt2 . Find the acceleration of the particle.

γ = gamma

Answered by admin @ 23/08/2021

Answer:

Acceleration, a = 2γ

Explanation:

The displacement x of a particle at time t along a straight line is given by,

$x=\alpha-\beta t+\gamma t^2$

We have to find the acceleration of particle. Th rate of change of velocity is called the acceleration of the particle. So, firstly we have to find the velocity with the displacement equation.

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

$v=\dfrac{d(\alpha-\beta t+\gamma t^2)}{dt}$

$v=-\beta+2\gamma t$

Now, $a=\dfrac{dv}{dt}$

$a=\dfrac{d(-\beta+2\gamma t)}{dt}$

$a=2\gamma$

Hence, the acceleration of the particle is 2γ.

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