Calculus and Velocity Models Assignment

Velocity Models 1
Calculus and Velocity Models
Author
Professor
University
City, State
Date

Velocity Models 2
Calculus and Velocity Models
1. Use calculus to model the velocity as a function of time
The velocity, distance and acceleration of an object falling from space are all
connected since the derivative of t he distance yield the instantaneous velocity of the while the
derivative of velocity yields the instatabeoius acceleration at a given point. Since the derivative
and finding the indefinite integral are reverse actions to each other, velocity as a function of time
can be established through finding the indefinite integral of a an acceleration as the function of
time.
a ( t )=∫ v ( t ) . dt
v ( t ) =∫ s ( t ) . dt
a ( t ) =∫−1342 ( t ) . dt
a ( t ) =∫−1342 t+ c
At a t=42s
V=1342
At t=0. V=0
But at vo = c1
Thus v ( t )=−1342 t+ vo
And s ( t )=−671 t2
t + vo+ s
Use integration to determine the expression for the velocity as a function of time
1. In the first 42 seconds of Felix Baumgartner’s fall, the only 2 forces acting on him as he
skydived are the gravitation pull of the earth which made him fall and the air resistance

Velocity Models 3
which had a tendency of pushing him upwards, against gravity From the physics of
projection, the velocity of the jump can be expressed in graphical manner. Since the first
42 seconds entail his jumping from outside of space, the air resistance tends to vary with
the speed of his mass falling from all the way in space. At the same time the impact of
gravity remains constant throughout his entire jump. The jumper will thus experience an
external force acting on his body that will vary the speed of the fall for the first 42
seconds. Because of this variation, a calculus model is the best mathematical tool to
express the variation between the velocity and time is a calculus model. This external
force can be established by obtaining the difference between the gravitational forces and
the air resistance , which will also vary with the difference in time.
F ( t )=Fg ( t )−FAR (t)
The constant gravitational forces that the jumper experiences during the time can be
obtained by the formula:
g ( t )= GM
r (t ')
Where G = gravitational constant between the space and the earth’s surface and
R = radius
M = is the mass.
The value of G is 6.67 x 10-11 m3 kg-1 s-2
And the mass of planet Mars is 639 x 1021 kg
And the radius of Mars is 3390 km. This radius continues to vary during the fall as the body of
the jumper approaches earth and the distance is reduced.
The g obtained which is the initial acceleration is 3.63m/s2
The force of acceleration can be given by the 2 formula of force,