Derivative table

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Derivative table
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If the displacement is described by
We want to find the velocity. See page A11 4
Or changing variables
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If the displacement is described by
To find the velocity. See page A11 9
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Estimate how far the object traveled between
initial and final time
..one second at 5m/s equals 5 meters plus one
second at 7m/s comes to 12 meters, plus
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Get a better estimate of the total distance by
using half second increments..
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How to achieve perfection? Infinitesimal time
intervals. Find the area under the curve.
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Definite integral- the area under the curve
between fixed values of the independent variable
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Managing the limits
Ending point at xxB
Starting point xxA
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Indefinite integrals
definite integrals
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two different curves having the same
derivative, different area.
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Page A11 Integral 9 we see an indefinite
integral
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Getting x from v
If v is v(t)
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Getting v from a
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Constant Acceleration, a special case
Eqn. 2-11 p. 23
Eqn. 2-15 p. 23
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Constant Acceleration, a special case cont.
Eqn. 2-11 p. 23
Eqn. 2-15 p. 23
Rewrite 2-15
Substitute 2-11 for (at) to get
or
Eqn. 2-17 p. 23
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Constant Acceleration, a special case cont.
Isolate t in Eqn. 2-11 p. 23
And substitute into 2-17
To get
or
Eqn. 2-16 p. 23
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900 ft cannon
From Earth to the Moon Jules Verne
Capsule is shot from
900ft1.0m/3.28ft274m
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The Civil Engineering
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The Projectile
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All the comforts of home
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Min velocity to reach Moon when shot from
Surface of earth 11,100 m/s
Boom!
How many gs???
224835 m/s2
23,000 gs
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It feels so good when You stop.
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A note about getting x from v
Must isolate the variables..get everything that
depends on x on one side, everything that depends
on t on the other.
Three cases
v(x)
v constant
v(t)