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Let's consider a
kinematics problem.

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And in this problem, we want to
focus on special conditions--

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how to think about that.

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So what I'm going to consider
is some charged plates,

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and I have a charged
particle, and it

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enters into this region
of charged plates.

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And in this problem,
there's two types

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of forces that are going
to act on this particle.

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There's a gravitational
force down.

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And we're going to talk
about some constant force

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upwards, whose magnitude
is changing in time.

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And what I'd like to do is
know what type of-- how strong

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does this force
have to be-- this b

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is a constant-- in order for the
particle to not hit the bottom?

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Now, let's think
about a little-- when

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we get started on a
problem like this,

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there's a number
of different issues

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that we have to think about.

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The first issue is that how do
we even sketch what we think

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will happen here?

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Well, a particle enters
at time t equals 0.

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So this force is initially
zero when the particle enters.

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So the particle is experiencing
gravitational force.

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And we should expect
it to move-- start

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to accelerate downwards.

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But then this force
is increasing in time.

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And so at a certain point,
these two forces will balance

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and the particle will
have no net force up.

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And gradually, this force
will increase so the particle

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will experience a force up.

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So we would expect
some type of motion

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where the particle
starts to go down.

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But now, it's starting to
feel that force upwards

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and it starts to maybe
move upwards like that.

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So what I've done
here is I've sketched

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a trajectory of
the motion to help

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me think about the problem.