The following figure shows the displacement time (x-t) graph of a body in motion. The ratio of the speed in first second and that in next two seconds is :
[amp_mcq option1=”1 : 2″ option2=”1 : 3″ option3=”3 : 1″ option4=”2 : 1″ correct=”option4″]
This question was previously asked in
UPSC CAPF – 2009
In the first second (from t=0 to t=1), the displacement changes from 0 to 3. The velocity is `(3 – 0) / (1 – 0) = 3/1 = 3` units/second. The speed in the first second (v1) is `|3| = 3`.
In the next two seconds (from t=1 to t=3), the displacement changes from 3 to 0. The velocity is `(0 – 3) / (3 – 1) = -3/2` units/second. The speed in the next two seconds (v2) is `|-3/2| = 3/2`.
The ratio of the speed in the first second and that in the next two seconds is `v1 : v2 = 3 : (3/2)`. To express this ratio in integers, we can multiply both parts by 2: `(3 * 2) : (3/2 * 2) = 6 : 3`. Dividing by 3, we get the simplified ratio `2 : 1`.