Question:

A particle moving with a uniform acceleration travels $24\, m$ and $64 \,m$ in the first two consecutive intervals of $4\,s$ each. Its initial velocity is

Updated On: Jul 28, 2022

1 m/s
10 m/s
5 m/s
2 m/s

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The Correct Option is A

Solution and Explanation

$s=u t+\frac{1}{2} a t^{2}$ for $\varepsilon t \,t=4 s$, $s=24\, m$ $\therefore 24=4 u+\frac{1}{2} a(4)^{2}$ or $8 a+4 u=24$ or $2 a+u=6 \ldots$(i) For $t=8 s$, $s=24+64=88 \,m$ $\therefore 88=8 u+\frac{1}{2} a(8)^{2}$ or $32 a+8 u=88$ or $4 a+u=11 \ldots$ (ii) Solving Eqs. (i) and (ii), we get initial velocity $u=1 \,m / s$.

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