First slide

Relative motion based problems

Question

Two cars A and B cross a point P with velocities 10m/s and 15 m/s. after that they move with different uniform accelerations and the car A overtakes B with a speed of 25 m/s. Their accelerations are in the ratio

Moderate

A

3 : 1
B

2 : 1
C

3 : 2
D

4 : 3

Solution

They have travelled for same distance for same time.
So, $s = \frac{(v_{1} + u_{1})}{2} t = (\frac{v_{2} + u_{2}}{2}) t$
$(10 + 25) = 15 + u_{2}$
$u_{2} = 20 m / s$
$\begin{array}{l} a_{1} = \frac{25^{2} - 10^{2}}{2 S} \\ a_{2} = \frac{20^{2} - 15^{2}}{2 S} a_{1} : a_{2} = 3 : 1 \end{array}$

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