Question

If the particle's motion is described as x=ut+1/2a1t^2, where x is position t is time and u&a are constant show that acceleration of the particle is constant​

Answer 1

Given:

The particle's motion is described as x=ut+½at², where x is position t is time and u and a are constant.

To prove:

Acceleration of the particle is constant.

Calculation:

Acceleration function opening object can be calculated by second order differentiation of the displacement function with respect to time.

$\therefore \: x = ut + \frac{1}{2} a {t}^{2}$

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

$= > v = \dfrac{d(ut + \frac{1}{2}a {t}^{2}) }{dt}$

$= > v = u + \dfrac{1}{2} a(2t)$

$= > v = u + at$

Performing 2nd order differentiation :

$= > acc. = \dfrac{dv}{dt}$

$= > acc. = \dfrac{d(u + at)}{dt}$

$= > acc. = 0 + a$

$= > acc. = a$

$= > acc. = constant$

So , Acceleration of the object is constant.

[Hence Proved].