Question

The motion of a particle is described by the equation y=ut+1/2gt2.Find out the acceleration of the particle.

Answer 1

y=ut+1/2gt².
dy/dt = d/dt ut + d/dt 1/2gt².
v=u+2gt
dv/dt= d/dt u + d/dt 2gt
a= 0+ 2g

Answer 2

Answer:

The acceleration of the particle, a = g

Explanation:

It is given that the motion of a particle is described by :

$y=ut+\dfrac{1}{2}gt^2$..............(1)

Where

y is the displacement

The rate of change of displacement per unit time is called the velocity of particle.

Differentiating equation (1) wrt t. We get,

$\dfrac{dy}{dt}=u+gt$

Since, $v=\dfrac{dy}{dt}$

$v=u+gt$............(2)

Again differentiating equation (2) wrt t. We get,

$\dfrac{dv}{dt}=\dfrac{du}{dt}+g$

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

And $\dfrac{du}{dt}=0$

So, $a=g$

So, the acceleration of the particle is g. Hence, this is the required solution.