The particle travels along the path defined by the parabola y=0.5x^2. If t

kolonelyf4 2021-11-07 Answered
The particle travels along the path defined by the parabola y=0.5x2. If the component of velocity along the x axis is vx = (5t) ft/s, where t is in seconds, determine the particle’s distance from the origin O and the magnitude of its acceleration when t = 1 s. When t = 0, x = 0, y = 0.
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Expert Answer

David Tyson
Answered 2021-11-08 Author has 19 answers
From the equation for vx we can get an equation for x:
x=2.5t2
We can insert that to find the equation for y as a function of time:
y=0.52.52t4=3.125t4
Distance at the t=1 is:
dx=2.5 ft
dy=3.125ft
d=dx+dy=2.52+3.1252
d=4 ft
Acceleration in t=1 is:
ay=37.5t=37.5 fts2
ax=5 fts2
a=ax+ay=52+37.52
a=37.83 fts2
Result: d=4 ft
a=37.83 fts2
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