Question

The displacement-Time graph for 2 particles A and B are straight lines inclined at angles of 30 degree and 60 degree with the time axis then the ratio of velocity is ______?​

Answer 1

Solution :

⏭ Given:

✏ The displacement-time graph for two particles A and B are straight lines inclined at angles of 30° and 60° with the time axis.

⏭ To Find:

✏ Velocity ratio of both particles

⏭ Concept:

✏ Velocity of particle is defined as ratio of displacement to the time.

⏭ Formula:

✏ Formula of velocity in terms of displacement and time is given by

$\bigstar \: \boxed{ \tt{ \pink{velocity = \dfrac{ \triangle{x}}{ \triangle{t}} = slope \: of \: graph = \tan \theta}}} \: \bigstar$

⏭ Calculation:

$\implies \sf \: \dfrac{v_1}{v_2} = \dfrac{ (\tan \theta)_A}{( \tan \theta)_B} \\ \\ \implies \sf \: \dfrac{v_1}{v_2} = \frac{ \tan 30 \degree}{ \tan60 \degree} = \dfrac{1}{ \sqrt{3} \times \sqrt{3} } \\ \\ \implies \: \boxed{ \tt{ \red{v_1 : v_2 = 1 : 3}}}$