A body covers $12 ext{ m}$ in the 2nd second and $20 ext{ m}$ in the 4th second. What is its initi

Question

A body covers $12	ext{ m}$ in the 2nd second and $20	ext{ m}$ in the 4th second. What is its initial velocity and acceleration?

Professor PC Thomas Classes · Answer

The distance covered in the $n$-th second is $s_n = u + \frac{a}{2}(2n - 1)$. For 2nd second: $12 = u + \frac{a}{2}(3)$. For 4th second: $20 = u + \frac{a}{2}(7)$. Subtracting the two equations gives $8 = 2a \implies a = 4	ext{ m/s}^2$. Substituting $a = 4$ in the first equation: $12 = u + 6 \implies u = 6	ext{ m/s}$.