Question

Two straight lines drawn on the same displacement time graph make angles ${45}^{\circ }$ and ${60}^{\circ }$ as shown. The ratio of the two velocities is

• A. $\sqrt{3}:1$
• B. 1 : 1
• C. 1 : 2
• D. $\sqrt{3}:2$

Answer 1

The correct option is A $\sqrt{3}:1$

Answer is A.

Velocity is the displacement per time. So, if the displacement - time graph of an object is steeper (that is, making greater angle with the time axis), it indicates that the object is moving with greater velocity. The object covers more distance in less time.
To find the velocity, we divide displacement by time. From the graph, we can find that displacement is the opposite side and time is the adjacent side of the right angle. So, the slope of the graph, that is, $tan\theta$, will give the velocity of the object.
Hence, the velocity ratio will be as follows.
$\frac{v_1}{v_2}=\frac{tan60}{tan45}=\sqrt{3}:1$.