The document discusses relative motion, defining it as the motion of an object concerning other moving or stationary objects. It presents equations for relative velocity and acceleration in one and two dimensions, illustrating various cases with examples. The document concludes with a summary of the relative motion principles governing interactions between two moving objects.

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