Question

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it on the first three seconds of its motion. The stone remains in the air for

• A. $6$ s
• B. $5$ s
• C. $7$ s
• D. $4$ s

Answer 1

The correct option is B $5$ s

Given that the stone falls from rest, hence $u=0$. Now, distance covered in the last second is equal to distance covered in the first three seconds of the motion.

Hence, $S_3=S_t$

$\Rightarrow S_3=0+\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times 9=45$

and so, $S_t=45=u+(2t-1)\frac{10}{2}$

$\Rightarrow 0+5(2t-1)=45$

$\Rightarrow t=5$ s