Question

A particle is moving in $xy$-plane with $y=x/2$ and $v_x=4-2t$. Choose the correct options.

• A. Initial velocities in x and y directions are negative
• B. Initial velocities in x and y directions are positive
• C. Motion is first retarded, then accelerated
• D. Motion is first accelerated, then retarded

Answer 1

Answer: (B), (C)

Initial velocities in x and y directions are positive
Motion is first retarded, then accelerated

$y=\frac{x}{2}$ implies that the particle is moving in a straight line passing through the origin.
$v_x=4-2t,v_x=u_x+a_{x}t,u_x=4,a_x=-2$
Now, $y=\frac{x}{2}\Rightarrow \frac{dy}{dt}=\frac{1}{2}\frac{dx}{dt}$
$v_y=\frac{1}{2}{v}_x=2-t,v_y=u_y+a_{y}t$,
$u_y=2$ and $a_y=-1$.