First slide

Relative motion based problems

Question

At time t = 0, two bodies A and B are at the same point. A moves with constant velocity V and B starts from rest and moves with constant acceleration a. Relative velocity of B with respect to A when the bodies meet each other is

Moderate

A

V/2
B

V/3
C

V
D

2V

Solution

After time t,
$x_{A}$ = Distance traversed by A = Vt
$x_{B}$ = Distance traversed by
$\large B = \frac{1} {2}at^2$

when the bodies meet, xA = xB

$\large \therefore vt = \frac{1} {2}at^2 \Rightarrow at = 2v$

Now after time 't' $v_{A}$ = velocity of A = V and $v_{B}$ = velocity of B = 0 + at = 2V

$\large \therefore$
$V_{B A}$ = velocity of B relative to A
= $v_{B}$ - $v_{A}$ = 2V-V = V

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