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

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

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\\ \text{Distance travelled in nth second is given as}: \\ s_{n}=u+a\left(n-\frac{1}{2}\right)$ \\ According to question, \\ $\mathrm{s}_{8}=\mathrm{u}+\mathrm{a}\left(8-\frac{1}{2}\right)=55$\\ or $u+\frac{15 a}{2}=55$ \\ or $2 \mathrm{u}+15 \mathrm{a}=110---(\mathrm{i})$ \\ and $s_{13}=u+a\left(13-\frac{1}{2}\right)=85$ \\ or $u+\frac{25 a}{2}=85$ \\ or $2 u+25 a=170---(\text { ii })$ \\ Solving equations (i) and (ii), we get \\ acceleration, $a=6 \mathrm{m} / \mathrm{s}^{2}$ \\ and initial velocity, $u=10 \mathrm{m} / \mathrm{s}$

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shubham.krishnan

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