The curvilinear motion of a particle is defined by 
and 
, where 
is in meters per second, 
is in meters, and 
is in seconds. It is also known that 
when 
. Determine its velocity and acceleration when the position 
is reached.
Text Solution
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The 
-coordinate is obtained by integrating the expression for 
, and the 
-component of the acceleration is obtained by differentiating 
. Thus,
The y-components of velocity and acceleration are
We now calculate corresponding values of 
and 
for various of 
and plot 
against 
to obtain the path as shown
When 
, so 
. For this value of the time, we have
The velocity and acceleration components and their resultants are shown on the separate diagram for point 
, where 
. Thus, for this condition we may write
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