Question

Determine the initial velocity and acceleration of particle travelling with uniform acceleration in a straight line if it travels 55m in the 8th second and 85m in the 13th second of its motion

Answer 1

Distance travelled by a particle travelling with uniform acceleration(a) and initial velocity(u) in a straight line in the $n^{th}$ second is given as

$S_n=u+ \frac{a}{2} \times (2n-1)$

given that $S_8=55m\ and\ S_1_3=85m$

$S_8=u+ \frac{a}{2} \times (2 \times 8-1)\\\\ \Rightarrow55=u+ \frac{15a}{2}\\\\ \Rightarrow55=u+7.5a$

$Similarly\\S_1_3=u+ \frac{a}{2} \times (2 \times 13-1)\\ \\ \Rightarrow85=u+ \frac{25a}{2}\\\\ \Rightarrow85=u+12.5a$

Subtracting second equation from the first, we get
30 = 5a
⇒ a = 30/5 = 6 m/s²

from the first equation,
$55=u+7.5a\\ \\ \Rightarrow55 = u+7.5 \times 6\\ \\ \Rightarrow55 = u+45\\ \\ \Rightarrow u=55-45=10\ m/s$

Acceleration is 6m/s² and the initial velocity is 10m/s.