Question

A particle projected from the origin $(x=y=0)$ moves in $xy$ plane so that its velocity is v = $(2\hat{i}+4x\hat{j})$ m/s, when it is at point (x,y) m.( $\hat{i}and\hat{j}$ are the unit vectors along $x$ and $y$ axis). What is the value of $y$, when $x=3$

• A. $15$
• B. $10$
• C. $9$
• D. $8$

Answer 1

The correct option is C $9$

$V_y=\frac{dy}{dt}=4x$

$V_x=\frac{dx}{dt}=2$
Hence, $x=2t$

$⟹y={\int }_0^{t}8tdt$
Hence , $y=4t^2$
At $x=3$ , $t=\frac{x}{2}=\frac{3}{2}$

At $t=\frac{3}{2},y=4t^2=4\times \frac{9}{4}=9$