Question

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

Answer 1

Answer:

The ratio is 1 : 3.

Explanation:

Now, the slope of position-time graph gives the velocity of the object ( derivative of position with respect to time ). So the straight lines have inclinations of 30° and 60° with the axis of time ( X-axis ).

So, the slopes will be,

$\tan(30) = \frac{1}{ \sqrt{3} }$

$\tan(60) = \sqrt{3}$

The ratio will be,

$\frac{ \frac{1}{ \sqrt{3} } }{ \sqrt{3} } = \frac{1}{3}$

Which indeed is 1:3 .