Question

The position-time graphs of two cars A and B are straight lines making angles 30° and 60° with the time axis respectively. The ratio of velocities of A and B is
(1) 1:√3
(2)√3:1
(3) 1:3
(4) 3:1

​

Answer 1

Concept : The slope of a position-time graph gives the velocity of the object. Straight-line means that the cars are moving with constant velocity. The slope is the tangent of the angle made by it through the horizontal.

Given : we are provided with the angles made by the slope of cars A and B which are 30° and 60° respectively

Let's calculate the ratio:

$\\\quad\longrightarrow\quad\sf \dfrac{V_{A}}{V_{B}} = \dfrac{\tan30}{\tan60}$

$\\\quad\longrightarrow\quad\sf \dfrac{V_{A}}{V_{B}} = \dfrac{1}{\sqrt{3} } \div \sqrt{3}$

$\\\quad\longrightarrow\quad\sf \dfrac{V_{A}}{V_{B}} = \dfrac{1}{\sqrt{3} } \times \dfrac{1}{\sqrt{3} }$

$\\\quad\longrightarrow\quad \boxed{\sf \dfrac{V_{A}}{V_{B}} = \dfrac{1}{3 } }\bigstar$

hence, option (3)!!