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Kinematic Equations: Derivation and Applications, Exercises of History

The derivation of three fundamental kinematic equations, which describe the motion of an object under the influence of constant acceleration. The equations relate the initial velocity (v0), final velocity (vf), acceleration (a), time (t), and displacement (h) of the object. The document demonstrates the step-by-step derivation of the third equation, v^2_f = v^2_0 + 2gh, which is a crucial relationship in the study of kinematics and the motion of objects. By understanding these equations and their derivations, students can gain a deeper understanding of the principles governing the motion of objects, which is essential in fields such as physics, engineering, and applied sciences. A valuable resource for students, researchers, and professionals interested in the fundamental concepts of kinematics and the analysis of object motion.

Typology: Exercises

2016/2017

Uploaded on 10/07/2022

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REYES DIEGO MARICARMEN
TAREA 1 : DEMOSTRAR V2
f=V2
o+ 2gh
t= (tfto)
a=g
Formula 1
Vf=V o +a(tfto)
Formula 2
h=vo(tfto) + 1
2a(tfto)2
Formula 3 (demostrar)
V2
f=V2o+ 2gh
De la ecuaci´on 1
Vf=V o +a(tfto)
tfto=vfvo
aEcuaci´on 4
la ecuacion 4 se remplaza en la ecuacion 2
h=vo(vfvo
a) + 1
2a(vfvo
a)2
h=vovf
a
v2
o
a+1
2
a[v2
f2vfvo+v2
o
a
2
h=
vovf
a
v2
o
a+v2
f
2a
2vfvo
2a+v2
o
2a
h=v2
f
2a
v2
o
2a=v2
fv2
o
2a
h=v2
fv2
o
2a
2ah =v2
fv2
o
v2
o+ 2ah =v2
f
V2
f=v2
o+ 2ah
V2
f=v2
o+ 2gh
1

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REYES DIEGO MARICARMEN

TAREA 1 : DEMOSTRAR V

2

f

= V

2

o

  • 2gh

t = (t f

− t o

a = g

Formula 1

V

f

= V o + a(t f

− t o

Formula 2

h = v o

(t f

− t o

a(t f

− t o

2

Formula 3 (demostrar)

V

2

f

= V

2

o + 2gh

De la ecuaci´on 1

V

f

= V o + a(t f

− t o

t

f

− t

o

v f

− v o

a

Ecuaci´on 4

la ecuacion 4 se remplaza en la ecuacion 2

h = v

o

v

f

− v

o

a

a(

v

f

− v

o

a

2

h =

v o

∗ v f

a

v

2

o

a

a[

v

2

f

− 2 v

f

∗ v

o

  • v

2

o

a 

2

h =

v o

∗ v f

a

v

2

o

a

v

2

f

2 a

2 v f

∗ v o

2 a

v

2

o

2 a

h =

v

2

f

2 a

v

2

o

2 a

v

2

f

− v

2

o

2 a

h =

v

2

f

− v

2

o

2 a

2 ah = v

2

f

− v

2

o

v

2

o

  • 2ah = v

2

f

V

2

f

= v

2

o

  • 2ah

V

2

f

= v

2

o

  • 2gh