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Relative motion
The motion of an object with
respect to other moving or
stationary object is called a
relative motion.
Relative motion in one dimension
Frame - A Frame - B Frame - C
xB/A xC/B
xC/A
xC/A = xB/A + xC/B
From above figure,
Differ...
Relative motion in one dimension
Car - A Car - B
vA vB
vA/B = vA − vB
Relative velocity of A w.r.t. B Relative velocity of...
𝐂𝐚𝐬𝐞 − 𝟏: 𝐯 𝐀 = 𝐯 𝐁
Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m)
0 10 25
5 15 30
10 20 35
15 25 40
20 30 45
25 35 50
5 10 15 20 25 30
t0
20
40...
𝐂𝐚𝐬𝐞 − 𝟐: 𝐯 𝐀 < 𝐯 𝐁
Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m)
0 10 20
5 15 30
10 20 40
15 25 50
20 30 60
25 35 70
5 10 15 20 25 30
t0
20
40...
𝐂𝐚𝐬𝐞 − 𝟑: 𝐯 𝐀 > 𝐯 𝐁
Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m)
0 10 30
5 20 35
10 30 40
15 40 45
20 50 50
25 60 55
5 10 15 20 25 30
t0
20
40...
Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m)
0 10 55
5 20 50
10 30 45
15 40 40
20 50 35
25 60 30
5 10 15 20 25 30
t0
20
40
60
x
0
10
30
50
A
B...
Relative motion in two dimension
Stationary
Frame - A
Frame - B
Frame - C
Constant velocity
acceleration
rB/A
rC/B
rC/A
Relative motion in two dimension
From above figure,
Differentiate eq.(1) w.r.t. time we get,
… … . . (1)
… … . . (2)
Now d...
Relative motion in two dimension
vA
vB
vA
−vB vB
−vA
vA/B vB/A
vA/B = vA − vB vB/A = vB − vA
Thank
you
Relative motion in 1D & 2D
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Relative motion in 1D & 2D

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This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.

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Relative motion in 1D & 2D

  1. 1. Relative motion The motion of an object with respect to other moving or stationary object is called a relative motion.
  2. 2. Relative motion in one dimension Frame - A Frame - B Frame - C xB/A xC/B xC/A xC/A = xB/A + xC/B From above figure, Differentiate eq.(1) w.r.t. time we get, … … . . (1) vC/A = vB/A + vC/B Stationary Constant velocity acceleration … … . . (2) Now differentiate eq.(2) w.r.t. time we get, aC/A = aB/A + aC/B The term aB/A is zero, because vB/A is constant aC/A = aC/B
  3. 3. Relative motion in one dimension Car - A Car - B vA vB vA/B = vA − vB Relative velocity of A w.r.t. B Relative velocity of B w.r.t. A vB/A = vB − vA
  4. 4. 𝐂𝐚𝐬𝐞 − 𝟏: 𝐯 𝐀 = 𝐯 𝐁 Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m) 0 10 25 5 15 30 10 20 35 15 25 40 20 30 45 25 35 50 5 10 15 20 25 30 t0 20 40 60 x 0 10 30 50 A B
  5. 5. 𝐂𝐚𝐬𝐞 − 𝟐: 𝐯 𝐀 < 𝐯 𝐁 Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m) 0 10 20 5 15 30 10 20 40 15 25 50 20 30 60 25 35 70 5 10 15 20 25 30 t0 20 40 60 x 0 10 30 50 A B
  6. 6. 𝐂𝐚𝐬𝐞 − 𝟑: 𝐯 𝐀 > 𝐯 𝐁 Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m) 0 10 30 5 20 35 10 30 40 15 40 45 20 50 50 25 60 55 5 10 15 20 25 30 t0 20 40 60 x 0 10 30 50 A B x t
  7. 7. Time (s) 𝐱 𝐀 (m) 𝐱 𝐁 (m) 0 10 55 5 20 50 10 30 45 15 40 40 20 50 35 25 60 30 5 10 15 20 25 30 t0 20 40 60 x 0 10 30 50 A B x t Two objects moving in opposite direction
  8. 8. Relative motion in two dimension Stationary Frame - A Frame - B Frame - C Constant velocity acceleration rB/A rC/B rC/A
  9. 9. Relative motion in two dimension From above figure, Differentiate eq.(1) w.r.t. time we get, … … . . (1) … … . . (2) Now differentiate eq.(2) w.r.t. time we get, The term aB/A is zero, because vB/A is constant rC/A = rB/A + rC/B vC/A = vB/A + vC/B aC/A = aB/A + aC/B aC/A = aC/B
  10. 10. Relative motion in two dimension vA vB vA −vB vB −vA vA/B vB/A vA/B = vA − vB vB/A = vB − vA
  11. 11. Thank you
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This PPT covers relative motion between particles in a very systematic and lucid manner. I hope this PPT will be helpful for instructor's as well as students.

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