Question

the displacement of an object along the three axis are given by $x=2t^2$, $y=t^2-4t$ and $z=3t$. The initial velocity of the particle is

• A. $10unit$
• B. $12unit$
• C. $5unit$
• D. $2unit$

Answer 1

The correct option is C $5unit$

We know,

Velocity is the slope of x-t graph,

$v_x=\frac{d\left(2t^2\right)}{dt}=4t$

$v_y=\frac{d(t^2-4t)}{dt}=2t-4$

$v_z=\frac{d\left(3t\right)}{dt}=3$

At $t=0$

$v_x=0,v_y=-4,v_z=3$

$v=\sqrt{v_x^2+v_y^2+v_z^2}=\sqrt{16+9}=\sqrt{25}=5$

Option $\text{C}$ is the correct answer