Question

The motion a particle is given by $y=Ut+\frac{1}{2}{gt}^2$. Whose $y$ is the displacement along $y$ is calculate what kind of acceleration the particle is going through.

Answer 1

$y=ut+\frac{1}{2}g{t}^2$

Differentiate it with respect to time t

$\frac{dy}{dt}=\frac{d}{dt}ut+\frac{d}{dt}\frac{1}{2}g{t}^2$

we get,

$v=u+2g$

on differentiating it,

$\frac{dv}{dt}=\frac{d}{dt}u+\frac{d}{dt}2gt$

$a=0+2g$

$a=2g$

So, Acceleration of the particle $=a=2g$