Relative Velocity
The relative velocity of the body comes into consideration when the other object moves either in the same or opposite direction. The speeds of the involved objects may be increasing, decreasing, or constant with reference to each other.
Let us assume the initial position of two objects A and B are both at origin, at points xA (0) and xB (0) respectively. The corresponding positions of these objects at time instance t will be equivalent to,
xA (t) = xA(0) + vAt
xB (t) = xB(0) + vBt
Displacement from object A to B is given by,
xB(t) – xA(t) = [xB (0) – xA (0)] + (vB -vA)t
The velocity of B relative to A is given by,
vBA = vB – vA
The velocity of A relative to B is given by,
vAB = vA – vB
The concept of relative velocity can be understood by following Position-Time graphs.
Position-Time Graphs Depicting Relative Velocity
The concept of relative velocity can be explained by the Position-Time graph using the following three cases.
Case 1: Two objects moving in the same direction with equal velocities.
In the above graph, the two objects will appear at rest with respect to one another.
Case 2: Two objects moving with different velocities in the same direction.
In the above graph,
- The magnitude of VBA and VAB will be lower than the magnitude of VA and VB. Object A appears faster than B.
- The velocities of the object will not be so large with respect to one another as compared to a stationary environment.
Case 3: Two objects moving with different velocities but in opposite directions.
In the above graph,
- The magnitude of VBA and VAB will be higher than the magnitude of VA and VB.
- Both objects will appear moving faster than one another.
Relative Motion
Relative Motion is defined as the motion of an object when observed with respect to another object which may be either at rest or in motion. The concept of motion is relative in nature rather than absolute. As per the definition of motion, a body is said to be in motion or at rest if it changes its position with respect to the observer or a stationary object. This can be understood from the following example
Example of Relative Motion: Suppose you and your friend are traveling on a train sitting together and a boy standing alongside the track is observing you. Both of you don’t change your position with respect to each other hence both of you are at rest with respect to each other but with respect to the boy who was standing outside you and your friend are in motion because your position is changing with time.
Table of Content
- Relative Motion Definition
- Relative Velocity
- Reference Frames
- Motion in One Dimension
- Relative Motion in One Dimension
- Motion in Two Dimensions
- Relative Motion in Two Dimensions
- Relative Motion Problems
Hence we observe that the state of motion is different for different observers making motion a relative concept rather. The difference in the observation of the boy standing outside and you sitting inside is because of the different Frames of Reference.