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# 13.4 Motion in Space: Velocity and Acceleration - magnitude of velocity vs velocity 13.4 Motion in Space: Velocity
and Acceleration
Motion in Space: Velocity and Acceleration
In this section we show how the ideas of tangent and
normal vectors and curvature can be used in physics to
study the motion of an object, including its velocity and
acceleration, along a space curve.
In particular, we follow in the footsteps of Newton by using
these methods to derive Kepler's First Law of planetary
motion.
2
Motion in Space: Velocity and Acceleration
Suppose a particle moves through space so that its
position vector at time t is r(t). Notice from Figure 1 that, for
small values of h, the vector
approximates the direction of
the particle moving along
the curve r(t).
Its magnitude measures the size Figure 1
of the displacement vector per
unit time.
3

How do you find the magnitude of velocity? How to calculate instantaneous velocity from a position-time graph. Plot the displacement function with respect to time. ... Choose any two points on the s-t graph. ... Find the line slope connecting the two points, i.e., between A and B. ... Repeat to find slope several times, moving B nearer to A. ... Calculate the slope for an infinitely small interval on the tangent line. ...

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