Question

Two bodies A and B are moving in the same direction with velocities VA and VB ,where VA>VB and they start symultaneously from different points, and B is in front of A. Represent their relative motion in a position time graph. Explain their relative velocity during the motion

Answer 1

Given that,

The velocity of A is greater than velocity of B.

We know that,

Relative velocity :

When the velocity of an object B in the rest frame of another object A. It is called relative velocity.

In mathematically form,

$V_{AB}=V_{A}-V_{B}$

When two bodies A and B are moving in the same direction with velocities $V_{A}$ and $V_{B}$

If $V_{A}> V_{B}$

B is in front of A it means

$v_{B}=-V_{B}$

We need to calculate the relative velocity

Using formula of relative velocity

$v_{AB}=v_{A}-v_{B}$

Put the value into the formula

$V_{AB}=V_{A}+V_{B}$

We draw the velocity of A and B in a position time graph.

Hence, The relative velocity is $V_{A}+V_{B}$

Answer 2

Given:

Two bodies A and B are moving in the same direction with velocities Va, and Vb, where Va is greater than Vb, and they start simultaneously from different points, and B is in front of A.  

To find:

Represent their relative motion in a position time graph. Explain their relative velocity during the motion

 

Solution:

From given, we have,

Two bodies A and B are moving in the same direction with velocities Va, and Vb, where Va is greater than Vb

The slope of the graph represents, dx/dt

we know that, the velocity, v = dx/dt

Thus, the velocity of Va > velocity of Vb

Relative velocity is the velocity of one body with respect to another body.  

V_{ba} = -V_{ab}

|V_{ba}| = |V_{ab}|

V_{ab} = Va - Vb        (as Va is greater than Vb)

The magnitude of V_{ab} and V_{ba} will be lower than the magnitudes of Va and Vb.