Solved: PHYSICS Question for NEET

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A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rd second?

7/5

5/7

7/3

3/7

Method 1: Galileo's Law of Odd Numbers For a particle starting from rest with uniform acceleration, the distances traversed during equal successive intervals of time are in the ratio of odd numbers: $1 : 3 : 5 : 7 : 9 \dots$ . Distance in 1st second $\propto 1$ Distance in 2nd second $\propto 3$ Distance in 3rd second $\propto 5$ Distance in 4th second $\propto 7$ Therefore, the ratio of the distance travelled in the 4th second to that in the 3rd second is $7:5$ or $7/5$ .
Method 2: Kinematic Formula Distance travelled in the $n$ -th second is given by $S_n = u + \frac{a}{2}(2n - 1)$ . Since the body starts from rest, $u = 0$ . $S_4 = \frac{a}{2}(2 \times 4 - 1) = \frac{7a}{2}$ . $S_3 = \frac{a}{2}(2 \times 3 - 1) = \frac{5a}{2}$ .

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