Equations from Integrated Relativistic Velocity and Acceleration Composition Copyright © 2004 Joseph A. Rybczyk
Following is a complete list of all of the equations used in and/or derived in the Integrated Relativistic Velocity and Acceleration Composition work. For ease of reference, all equations are identified by the same number originally assigned in the theory. Also included are examples using the same Figures including the originally assigned numbers from the referenced work. 1. Summary List of All Formulas Used in the Above Referenced Paper
NRP =
vc t
va = and 1
11
vc t
va = (1) Constant Acceleration Formulas
vctav = and (2) Instantaneous Speeds from Acceleration 111 vc tav =
cvcTtv
22 −= and
cvc
Ttv
21
2
1−
= (3) Time Transformation Formulas
22 )( TacTcav
c
c
+= and
21
21
1)( Tac
Tcavc
c
+= (4) Instantaneous Speed Formulas
cvc
Vvv u
21
2
21−
+= (5) Velocity Composition Formula (Vu2 intentionally shown as V2 in paper)
21
21
2)(
vc
vvcVu−
−= (6) Velocity Composition Formula for Vu2
TtVv v
uu1
22 = (7) Equivalent Speed Relative to SF
cvc
Uvu2
12
21−
+= (8) Velocity Composition Formula Modified
21
21
2)(
vc
vucU−
−= (9) Velocity Composition Formula for U2
TtUu v1
22 = (10) Uniform Motion Speed Relative to SF
1
cuc
Vuv u
21
2
21−
+= (11) Velocity Composition Formula Modified
21
21
2)(
uc
uvcVu−
−= (12) Velocity Composition Formula for Vu2
cuc
Ttu
21
2
1−
= (13) Time Transformation Formula for UF u1
TtVv u
uu1
22 = (14) Uniform Motion Speed Relative to SF
cuc
Uuu2
12
21−
+= (15) Velocity Composition Formula, Standard Form
21
21
2)(
uc
uucU−
−= (16) Velocity Composition for U2
TtUu u1
22 = (17) Uniform Motion Speed Relative to SF
22 vcccvTDa
−+= and
22
2
)( TaccTcaD
c
ca
++= (18) Acceleration Distance for v & ac
21
2
11
vcc
TcvDa−+
= and 2
12
21
1)( Tacc
TcaDc
ca
++= (19) Acceleration Distance for v1 & ac1
22
2
122
Vcc
tcVD va
−+= and
212
2
212
2)( vc
vca
tacctcaD
++= (20) Acceleration Distance for V2 & ac2
22
21
221
2
22
av
av
DtcDtcV+
= (21) Instantaneous Speed, V2 using Da2
12 aaa DDD −= (22) The Relationship of Da2 to Da and Da1
21
21
211
2
2 )()(2
aav
aav
DDtcDDtcV
−+−
= (23) Instantaneous Speed, V2 using Da and Da1
2
2
22
vc t
Va = (24) Acceleration Rate, ac2
cVc
tt vv
22
2
12−
= (25) UF v2 Time Transformation
2
22
vu
ucu t
Va = (26) Acceleration Rate, acu2
cVc
tt uvvu
22
2
12−
= (27) UF vu2 Time Transformation
21
22
1
221
2
2
2
)()( vc
vvvcT
cacu
+−−−
= (28) Acceleration Rate, acu2 based on v and v1 (New)
)(1 2
1222
2
42
vcTac
cV
cu
u
−+
= (29) Alternate Formula for Vu2 (New)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+−
−+=
21
21
222vcc
cvvcc
cvTDa (30) Formula for Da2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛+
−+
+−
−+= 22
12
2222
)(u
ua V
vcc
Vvcvcc
cvTD (31) Formula for Da2 Based on Vu2 (New)
22
212
2
u
vuau
Vcc
tcVD−+
= and 2
122
212
2)( vcu
vcuau
tacctcaD
++= (32) Acceleration Distance for Vu2 & acu2
TtVv v1
22 = (33) Equivalent Speed Relative to SF
uTDu = (34) Uniform Motion Distance for u
21
21
211
2
2 )()(2
auv
auv
DDtcDDtcV
−+−
= (35) Instantaneous Speed, V2 using Du and Da1
3
cucTtu
22 −= (36) Time Transformation for UF u
21
21
1
vca
cvTc −
= (37) SF Interval for Reaching Speed v1
221 uca
cuTc
i−
= (38) Intermediate SF Interval for Reaching Speed u
21
21
2)(
vc
vucVu−
−= (39) Modified Velocity Composition Formula for Vu2
cVc
tt uuvu
22
2
12−
= (40) UF vu2 Time Transformation
TuDu 11 = (41) Uniform Motion Distance for u1
21
21
211
2
2 )()(2
auu
auu
DDtcDDtcV
−+−
= (42) Instantaneous Speed, V2 using Du1 and Da
TtVv u1
22 = (43) Equivalent Speed Relative to SF
22
2
122
Vcc
tcVD ua
−+= and
212
2
212
2)( uc
uca
tacctcaD
++= (44) Acceleration Distance for V2 & ac2
22
212
2
u
uuau
Vcc
tcVD−+
= and 2
122
212
2)( ucu
ucuau
tacctcaD
++= (45) Acceleration Distance for Vu2 & acu2
cVc
tt uv
22
2
12−
= (46) UF v2 Time Transformation
21
21
2)(
uc
uucVu−
−= (47) Velocity Composition for Vu2
cuc
Vuu u
21
2
21−
+= (48) Velocity composition formula
4
21
21
211
2
2 )()(2
uuu
uuu
DDtcDDtcV
−+−
= (49) Instantaneous Speed, V2 using Du and Du1
212
212
2)( ucu
ucuu
tactcaV
+= (50) Instantaneous Speed, Vu2
212
212
2)( uc
uc
tactcaV
+= (51) Instantaneous Speed, V2
23
2
133
Vcc
tcVD ua
−+= and
213
2
213
3)( uc
uca
tacctcaD++
= (52) Acceleration Distance for V3 & ac3
21
22
21
2
32
uucuccu
V−+−
= (53) Instantaneous Speed, V3 using u and u1 (New)
3
33
vc t
Va = (54) Acceleration Rate, ac3
cVc
tt uv
23
2
13−
= (55) UF v3 Time Transformation
213
213
3)( uc
uc
tactcaV
+= (56) Instantaneous Speed, V3
TtVv u1
33 = (57) Equivalent Speed Relative to SF
22
22ucucv
+= (58) Instantaneous Speed, v using u
1utTvV = (59) Equivalent Speed Relative to UF u1
2. Examples of Formula Applications
5
2.1 Case 1 – Two Different Acceleration Rates
FIGURE 6 Case 1 – Part 2 – The ac2 Relationship to ac1 and ac
Da Da1
v & Vu2
v1
ac1
ac
Distance in LY’s (SF)
Spe
ed (
SF)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5
Spe
ed (
UF
v 1) .5c
.25c
0
V2 ac2
Da2
0.1 0.2 0.3 Distance in LY’s (UF v1)
Where, relative to the SF,
ac and ac1 are constant rates of acceleration, v and v1 are the respective speeds, Da and Da1 are the respective distances, and, T is the time interval,
while, relative to UF v1, ac2 is a constant rate of acceleration, V2 is the speed,
v2 is the corresponding speed in the SF, Da2 is the corresponding distance in the SF, and,
tv1 is the time interval corresponding to T, while, tv and tv2 are the time intervals in UFs v and v2 respectively, (not shown in the
illustration) Given: c, ac, ac1, and T
22 )( TacTcav
c
c
+= and
21
21
1)( Tac
Tcavc
c
+= (4) Instantaneous Speed Formulas
6
cvcTtv
22 −= and
cvc
Ttv
21
2
1−
= (3) Time Transformation Formulas
v
c tva = and
1
11
vc t
va = (1) Constant Acceleration Formulas
vctav = and (2) Instantaneous Speeds from Acceleration 111 vc tav =
22 vcccvTDa
−+= and
22
2
)( TaccTcaD
c
ca
++= (18) Acceleration Distance for v & ac
21
2
11
vcc
TcvDa−+
= and 2
12
21
1)( Tacc
TcaDc
ca
++= (19) Acceleration Distance for v1 & ac1
12 aaa DDD −= (22) The Relationship of Da2 to Da and Da1
22
21
221
2
22
av
av
DtcDtcV+
= (21) Instantaneous Speed, V2 using Da2
21
21
211
2
2 )()(2
aav
aav
DDtcDDtcV
−+−
= (23) Instantaneous Speed, V2 using Da and Da1
Note, in the following, tv2 is the interval in UF v2 (not shown in the illustration)
corresponding to tv1
cVc
tt vv
22
2
12−
= (25) UF v2 Time Transformation
2
22
vc t
Va = (24) Acceleration Rate, ac2
TtVv v1
22 = (33) Equivalent Speed Relative to SF
22
2
122
Vcc
tcVD va
−+= and
212
2
212
2)( vc
vca
tacctcaD
++= (20) Acceleration Distance for V2 & ac2
7
FIGURE 7 Case 1 – Part 2 – The acu2 Relationship to ac1 and ac
Da Da1
v
v1
ac1
ac
Distance in LY’s (SF)
Spe
ed (
SF)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5
Spe
ed (
UF
v 1) .5c
.25c
0
Vu2
acu2
Dau2
0.1 0.2 0.3 Distance in LY’s (UF v1)
and also, relative to UF v1,
acu2 is a constant rate of acceleration, Vu2 is the speed,
vu2 is the corresponding speed in the SF, Dau2 is the corresponding distance in the SF, and,
whereas, tvu2 is the time interval in UF vu2 (not shown in illustration) corresponding to tv1,
cvc
Vvv u
21
2
21−
+= (5) Velocity Composition Formula (Vu2 intentionally shown as V2 in paper)
21
21
2)(
vc
vvcVu−
−= (6) Velocity Composition Formula for Vu2
TtVv v
uu1
22 = (7) Equivalent Speed Relative to SF
cVc
tt uvvu
22
2
12−
= (27) UF vu2 Time Transformation
8
2
22
vu
ucu t
Va = (26) Acceleration Rate, acu2
21
22
1
221
2
2
2
)()( vc
vvvcT
cacu
+−−−
= (28) Acceleration Rate, acu2 based on v and v1 (New)
)(1 2
1222
2
42
vcTac
cV
cu
u
−+
= (29) Alternate Formula for Vu2 (New)
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+−
−+=
21
21
222vcc
cvvcc
cvTDa (30) Formula for Da2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛+
−+
+−
−+= 22
12
2222
)(u
ua V
vcc
Vvcvcc
cvTD (31) Formula for Da2 Based on Vu2 (New)
22
212
2
u
vuau
Vcc
tcVD−+
= and 2
122
212
2)( vcu
vcuau
tacctcaD
++= (32) Acceleration Distance for Vu2 & acu2
2.2 Case 2 – Low Instantaneous Speed vs. High Uniform Speed
Where, relative to the SF, ac1 is a constant rate of acceleration, v1 is the achieved speed, u is a uniform rate of speed ≥ v1Da1 and Du are the respective distances, and, T is the time interval,
while, relative to UF v1, acu2 and ac2 are constant rates of acceleration, Vu2 and V2 are the respective speeds, Dau2 and Da2 are the respective SF distances,
vu2 and v2 are the respective corresponding speeds in the SF, U2 is the speed corresponding to u, u2 is the corresponding speed for U2 in the SF,
tv1 is the time interval corresponding to T, whereas, tvu2, tv2 and tu are the time intervals in UFs vu2, v2, and u respectively (not shown
in the illustration)
Given: c, u, ac1, and T
9
21
21
1)( Tac
Tcavc
c
+= (4) Instantaneous Speed Formula
cvc
Ttv
21
2
1−
= (3) Time Transformation Formula
1
11
vc t
va = (1) Constant Acceleration Formula (not shown in paper)
111 vc tav = (2) Instantaneous Speed from Acceleration (not shown in paper)
FIGURE 8 Case 2 – Part 2 – The ac2 and acu2 Relationships to ac1 and u
Da1
v1
ac1
Distance in LY’s (SF)
Spe
ed (
SF)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5
Spe
ed (
UF
v 1) .5c
.25c
0
u & U2
Du
0.1 0.2 0.3 Distance in LY’s (UF v1)
ac2
Da2
c
.75c
Dau2
acu2
V2
Vu2
10
cvc
Uvu2
12
21−
+= (8) Velocity Composition Formula Modified
21
21
2)(
vc
vucU−
−= (9) Velocity Composition Formula for U2
TtUu v1
22 = (10) Uniform Motion Speed Relative to SF
Given, Vu2 = U2,
cVc
tt uvvu
22
2
12−
= (27) UF vu2 Time Transformation
2
22
vu
ucu t
Va = (26) Acceleration Rate, acu2
22
212
2
u
vuau
Vcc
tcVD−+
= and 2
122
212
2)( vcu
vcuau
tacctcaD
++= (32) Acceleration Distance for Vu2 & acu2
uTDu = (34) Uniform Motion Distance for u
21
2
11
vcc
TcvDa−+
= and 2
12
21
1)( Tacc
TcaDc
ca
++= (19) Acceleration Distance for v1 & ac1
21
21
211
2
2 )()(2
auv
auv
DDtcDDtcV
−+−
= (35) Instantaneous Speed, V2 using Du and Da1
TtVv v1
22 = (33) Equivalent Speed Relative to SF
cVc
tt vv
22
2
12−
= (25) UF v2 Time Transformation
2
22
vc t
Va = (24) Acceleration Rate, ac2
22
2
122
Vcc
tcVD va
−+= and
212
2
212
2)( vc
vca
tacctcaD
++= (20) Acceleration Distance for V2 & ac2
11
cucTtu
22 −= (36) Time Transformation for UF u
2.3.1 Case 3 – The ac2 and acu2 Relationships to u and ac1
Da1 Du
Da2
FIGURE 9 Case 3 – Part 2 – The ac2 and acu2 Relationships to u and ac1
Distance in LY’s (SF)
Spe
ed (
SF)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5 S
peed
(U
F u)
.5c
.25c
0 0.1 0.2
Distance in LY’s (UF u) ac1
u
ac2
V2
.75c
c
0.3 0.4
acu2
ac2
v1 Vu2
Where, relative to the SF,
ac1 is a constant rate of acceleration, v1 is the achieved speed, u is a uniform rate of speed ≥ v1Da1 and Du are the respective distances, and, T is the time interval,
while, relative to UF v1, acu2 and ac2 are constant rates of acceleration, Vu2 and V2 are the respective speeds, Dau2 and Da2 are the respective SF distances,
12
vu2 and v2 are the respective corresponding speeds in the SF, U2 is the speed corresponding to u, u2 is the corresponding speed for U2 in the SF,
tv1 is the time interval corresponding to T, whereas, tvu2, tv2 and tu are the time intervals in UFs vu2, v2, and u respectively (not shown
in the illustration)
Given: c, u, ac1, and T
21
21
1)( Tac
Tcavc
c
+= (4) Instantaneous Speed Formula
21
21
1
vca
cvTc −
= (37) SF Interval for Reaching Speed v1
221 uca
cuTc
i−
= (38) Intermediate SF Interval for Reaching Speed u
cvc
Vvu u
21
2
21−
+= (60) Velocity Composition Formula Modified (not given in paper)
21
21
2)(
vc
vucVu−
−= (39) Modified Velocity Composition Formula for Vu2
cvc
Ttv
21
2
1−
= (3) Time Transformation Formulas
TtVv v
uu1
22 = (7) Equivalent Speed Relative to SF
cVc
tt uvvu
22
2
12−
= (27) UF vu2 Time Transformation
2
22
vu
ucu t
Va = (26) Acceleration Rate, acu2
22
212
2
u
vuau
Vcc
tcVD−+
= and 2
122
212
2)( vcu
vcuau
tacctcaD
++= (32) Acceleration Distance for Vu2 & acu2
uTDu = (34) Uniform Motion Distance for u
13
21
2
11
vcc
TcvDa−+
= and 2
12
21
1)( Tacc
TcaDc
ca
++= (19) Acceleration Distance for v1 & ac1
21
21
211
2
2 )()(2
auv
auv
DDtcDDtcV
−+−
= (35) Instantaneous Speed, V2 using Du and Da1
TtVv v1
22 = (33) Equivalent Speed Relative to SF
cVc
tt vv
22
2
12−
= (25) UF v2 Time Transformation
2
22
vc t
Va = (24) Acceleration Rate, ac2
22
2
122
Vcc
tcVD va
−+= and
212
2
212
2)( vc
vca
tacctcaD
++= (20) Acceleration Distance for V2 & ac2
cucTtu
22 −= (36) Time Transformation for UF u
2.3.2 Case 3 – The ac2 and acu2 Relationships to u1 and ac
Where, relative to the SF,
ac is a constant rate of acceleration, v is the achieved speed, u1 is a uniform rate of speed ≤ v Da and Du1 are the respective distances, and, T is the time interval,
while, relative to UF u1, acu2 and ac2 are constant rates of acceleration, Vu2 and V2 are the respective speeds, Dau2 and Da2 are the respective SF distances,
vu2 and v2 are the respective corresponding speeds in the SF, tu1 is the time interval corresponding to T,
whereas, tvu2, tv2 and tv are the time intervals in UFs vu2, v2, and v respectively (not shown in the illustration)
Given: c, u1, ac, and T
14
FIGURE 10 Case 3 – Part 2 – The ac2 and acu2 Relationships to u1 and ac
Du1
Da
v
u1
ac
Distance in LY’s (SF)
Spe
ed (
SF)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5
Spe
ed (
UF
u 1) .5c
.25c
0 0.1 0.2
Distance in LY’s (UF u1)
Da2 = 0 (Final)
acu2
ac2
- 0.1
Dau2
V2
Vu2
Da2 (Initial)
22 )( TacTcav
c
c
+= (4) Instantaneous Speed Formula
cuc
Vuv u
21
2
21−
+= (11) Velocity Composition Formula Modified
21
21
2)(
uc
uvcVu−
−= (12) Velocity Composition Formula for Vu2
cuc
Ttu
21
2
1−
= (13) Time Transformation Formula for UF u1
TtVv u
uu1
22 = (14) Uniform Motion Speed Relative to SF
cVc
tt uuvu
22
2
12−
= (40) UF vu2 Time Transformation
15
2
22
vu
ucu t
Va = (26) Acceleration Rate, acu2
22
212
2
u
uuau
Vcc
tcVD−+
= and 2
122
212
2)( ucu
ucuau
tacctcaD
++= (45) Acceleration Distance for Vu2 & acu2
TuDu 11 = (41) Uniform Motion Distance for u1
22 vcccvTDa
−+= and
22
2
)( TaccTcaD
c
ca
++= (18) Acceleration Distance for v & ac
21
21
211
2
2 )()(2
auu
auu
DDtcDDtcV
−+−
= (42) Instantaneous Speed, V2 using Du1 and Da
TtVv u1
22 = (43) Equivalent Speed Relative to SF
cVc
tt uv
22
2
12−
= (46) UF v2 Time Transformation
2
22
vc t
Va = (24) Acceleration Rate, ac2
22
2
122
Vcc
tcVD ua
−+= and
212
2
212
2)( uc
uca
tacctcaD
++= (44) Acceleration Distance for V2 & ac2
cvcTtv
22 −= (61) Time Transformation for UF v (not given in paper)
2.4. Case 4 – The ac2 and acu2 Relationships to u1 and u
Where, relative to the SF,
u is a uniform rate of speed u1 is a uniform rate of speed < u Du and Du1 are the respective distances, and, T is the time interval,
while, relative to UF u1, acu2 and ac2 are constant rates of acceleration, Vu2 and V2 are the respective speeds, Dau2 and Da2 are the respective SF distances,
16
vu2 and v2 are the respective corresponding speeds in the SF, U2 is the speed corresponding to u, u2 is the corresponding speed for U2 in the SF,
tu1 is the time interval corresponding to T, whereas, tvu2, tv2 and tu are the time intervals in UFs vu2, v2, and u respectively (not shown
in the illustration)
Given c, u, u1 and T
FIGURE 13 Case 4 – Part 2 – Two Different Uniform Motion Speeds
u1
Distance in LY’s (SF)
Spe
ed (
SF)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5 S
peed
(U
F u 1
) .5c
.25c
0
u & U2
Du
Du1
.75c
acu2
ac2
Vu2
V2
Da2
Dau2
cuc
Uuu2
12
21−
+= (15) Velocity Composition Formula, Standard Form
21
21
2)(
uc
uucU−
−= (16) Velocity Composition for U2
cuc
Ttu
21
2
1−
= (13) Time Transformation Formula for UF u1
17
TtUu u1
22 = (17) Uniform Motion Speed Relative to SF
uTDu = (34) Uniform Motion Distance for u
TuDu 11 = (41) Uniform Motion Distance for u1
cuc
Vuu u
21
2
21−
+= (48) Velocity composition formula
21
21
2)(
uc
uucVu−
−= (47) Velocity Composition for Vu2
TtVv u
uu1
22 = (14) Uniform Motion Speed Relative to SF
cVc
tt uuvu
22
2
12−
= (40) UF vu2 Time Transformation
2
22
vu
ucu t
Va = (26) Acceleration Rate, acu2
22
212
2
u
uuau
Vcc
tcVD−+
= and 2
122
212
2)( ucu
ucuau
tacctcaD
++= (45) Acceleration Distance for Vu2 & acu2
21
21
211
2
2 )()(2
uuu
uuu
DDtcDDtcV
−+−
= (49) Instantaneous Speed, V2 using Du and Du1
TtVv u1
22 = (43) Equivalent Speed Relative to SF
cVc
tt uv
22
2
12−
= (46) UF v2 Time Transformation
2
22
vc t
Va = (24) Acceleration Rate, ac2
18
22
2
122
Vcc
tcVD ua
−+= and
212
2
212
2)( uc
uca
tacctcaD
++= (44) Acceleration Distance for V2 & ac2
212
212
2)( ucu
ucuu
tactcaV
+= (50) Instantaneous Speed, Vu2
212
212
2)( uc
uc
tactcaV
+= (51) Instantaneous Speed, V2
cucTtu
22 −= (36) Time Transformation for UF u
3. Extrapolation of Principles
v
V3
ac3
ac
FIGURE 14 Extrapolation of Principles
u1
Distance in LY’s (SF)
Spee
d (S
F)
0
0.1
.75c
0
.25c
.5c
c
0.2 0.3 0.4 0.5
Spee
d (U
F u 1
)
.5c
.25c
0
u & U2
Du Da
Du1
.75c
acu2
ac2 Vu2
V2
Da2
Dau2
c
Du Da3
0.1 0.2 0.3 0.4
Where, relative to the SF,
u is a uniform rate of speed
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u1 is a uniform rate of speed < u Du and Du1 are the respective distances, ac is a constant rate of acceleration, v is the achieved speed, Da is the distance, and, T is the time interval,
while, relative to UF u1, acu2, ac2 and ac3 are constant rates of acceleration, Vu2, V2 and V3 are the respective speeds, Dau2, Da2 and Da3 are the respective SF distances,
vu2, v2 and v3 are the respective corresponding speeds in the SF, U2 is the speed corresponding to u, u2 is the corresponding speed for U2 in the SF,
tu1 is the time interval corresponding to T, whereas, tvu2, tv2, tv3 and tu are the time intervals in UFs vu2, v2, v3 and u respectively (not
shown in the illustration)
Given: c, u, u1 and T
uTDu = (34) Uniform Motion Distance for u
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22
21
2
32
uucuccu
V−+−
= (53) Instantaneous Speed, V3 using u and u1 (New)
cuc
Ttu
21
2
1−
= (13) Time Transformation Formula for UF u1
cVc
tt uv
23
2
13−
= (55) UF v3 Time Transformation
3
33
vc t
Va = (54) Acceleration Rate, ac3
23
2
133
Vcc
tcVD ua
−+= and
213
2
213
3)( uc
uca
tacctcaD++
= (52) Acceleration Distance for V3 & ac3
213
213
3)( uc
uc
tactcaV
+= (56) Instantaneous Speed, V3
TtVv u1
33 = (57) Equivalent Speed Relative to SF
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22
22ucucv
+= (58) Instantaneous Speed, v using u
cvcTtv
22 −= (3) Time Transformation Formula
vc t
va = (1) Constant Acceleration Formula
22 )( TacTcav
c
c
+= (4) Instantaneous Speed Formulas
1utTvV = (59) Equivalent Speed Relative to UF u1
Equations from Integrated Relativistic Velocity and Acceleration Composition
Copyright © 2004 Joseph A. Rybczyk
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