The particle travels along the path described as the path of a parabola
y = 0.25x^{2}. If the components of velocity along the y-axis
is v_{y} = t^{2} ft/s where t is in seconds, determine
the particle's distance from the origin O when t = 1s.

1) 2.5 ft
2) 1.2 ft
3) 3.4 ft
4) 5 ft

The particle's vertical
component is v_{y} = t^{2} ft/s,so integrating the equation
from time zero to t seconds
Substuting in the equation given, y = 0.25x^{2}

So, the particles distance from the origin is 1.20 ft.