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.

2. Relative motion
The motion of an object with
respect to other moving or
stationary object is called a
relative motion.

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. Relative motion in two dimension
Stationary
Frame - A
Frame - B
Frame - C
Constant velocity
acceleration
rB/A
rC/B
rC/A

10. 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

11. Relative motion in two dimension
vA
vB
vA
−vB vB
−vA
vA/B vB/A
vA/B = vA − vB vB/A = vB − vA

12. Thank
you