Question

A particle moves in a straight line so that x =√t then its acceleration is proportional to

Answer 1

here by using
$s = ut + 1 \div 2at {2} \:$
we find that a is directly proportion to ✓t or a=V-U/t if u=0 then a =V/t which is equals to ✓t now see the picture

Answer 2

Answer:

$a\propto t^{-3/2}$

Explanation:

The particle moves in a straight line is given by :

$x=\sqrt{t}$

Firstly calculating the velocity as :

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

$v=\dfrac{d(\sqrt{t})}{dt}$

$v=\dfrac{1}{2\sqrt t}$

Now calculating the acceleration of the particle as,

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

$a=\dfrac{d(\dfrac{1}{2\sqrt t})}{dt}$

$a=\dfrac{d(1/2\sqrt t)}{dt}$

$a=\dfrac{-1}{4}\dfrac{1}{t^{3/2}}$

So, $a\propto t^{-3/2}$

Hence, this is the required solution.