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13.4 Motion in Space: Velocity

and Acceleration

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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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