Introduction This section describes the principles and concepts related to the experiment. It is used to help the person reading
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First compute the resultant force F:
Then use Newton's second law to determine the acceleration vector for the particle:
Let and
denote the particle's position and velocity vectors, respectively.
(a) Use the fundamental theorem of calculus. The particle starts at rest, so . Then the particle's velocity vector at <em>t</em> = 10.4 s is
If you don't know calculus, then just use the formula,
So, for instance, the velocity vector at <em>t</em> = 10.4 s has <em>x</em>-component
(b) Compute the angle for
:
so that the particle is moving at an angle of about 313º counterclockwise from the positive <em>x</em> axis.
(c) We can find the velocity at any time <em>t</em> by generalizing the integral in part (a):
Then using the fundamental theorem of calculus again, we have
where is the particle's initial position. So we get
So over the first 10.4 s, the particle is displaced by the vector
or a net distance of about 395 m away from its starting position, in the same direction as found in part (b).
(d) See part (c).