Question # A particle located at ( x=0 ) at time ( t=0, ) starts moving along the positive ( X ) -direction with a velocity ( v=alpha sqrt{x} ). The displacement of the particle varies with time as:

# A particle located at ( x=0 ) at time ( t=0, ) starts moving along the positive ( X ) -direction with a velocity ( v=alpha sqrt{x} ). The displacement of the particle varies with time as:

(a) ( t^{3} )

(b) ( t^{2} )

(c) ( t )

(d) ( t^{1 / 2} ).

Solution

( V=a sqrt{x} )

( frac{d x}{d t}=8 a sqrt{x} )

( frac{d x}{sqrt{x}}=a d t Rightarrow ) in tegreating we ges

( 2 x^{frac{1}{2}}=a+ )

( x=left(frac{a}{2}right)^{2}+2 )