Question

The path of a particle is defined by y = 0.5x2. If the component of its velocity along the x-axis at x = 2 m is vx = 1 m/s, its velocity component along the y-axis at this position is ____.

Answer 1

Answer:

Velocity component along y-axis is 2 m/s.

Explanation:

Given that

$y=0.2x^{2}--(1)\\\v_{y}=?$

Differentiating (1) w.r.to t

$\frac{dy}{dt}=\frac{d}{dt}(0.5x^{2})\\\\\frac{dy}{dt}=(0.5)(2x)\frac{dx}{dt}\\\\v_{y}=xv_{x}\\\\At\,x=2 ,\,v_{x}=1\,m/s\\\\v_{y}=2\,m/s$

Velocity component along y-axis is 2 m/s.