Question

A ball falls freely from rest. The ratio of the distances travelled in first, second, third and fourth second is

Answer 1

As per the question, the ball is falling freely under gravity.

The initial velocity of the ball [u] = 0.

As the ball is under free fall, the acceleration produced on the ball is nothing else than acceleration due to gravity i.e g.

Let the distance travelled by the ball is denoted as S and time is denoted as t.

As per equation of kinematics, we know that-

                                                   $S= ut+\frac{1}{2} at^2$

                                                   $-S=\ 0*t+\frac{1}{2} [-g]t^2$

                                                   $S =\frac{1}{2} gt^2$

                                                   $S\ \alpha\ t^2$

Hence, the ratio of distance travelled by the ball in first, second, third and fourth seconds are-

         $S_{1}: S_{2}: S_{3}:S_{4} =t_{1}^2: t_{2}^2: t_{3}^2: t_{4}^2$

                                                    $=1^{2}: 2^{2}: 3^{2}: 4^{2}$

                                                    $=1:4:9:16$  [ans]