201907271536 Solution to 1991-CE-PHY-II-4

$T=\displaystyle{\frac{1}{f}}=1/5=0.2\,\mathrm{s}$ when $f=5\,\mathrm{Hz}$ .

Setup.

Given that from the figure.

Doing substitution for $s$ , $u$ , $a$ , and $t$ in

$s=ut+\displaystyle{\frac{1}{2}}at^2$ ,

I have some equations:

$\begin{aligned} 4 &= s_2 = u_1T + \frac{1}{2}aT^2 \\ 12 &= s_3 = u_1(2T) + \frac{1}{2}a(2T)^2 \\ 24 &= s_4 = u_1(3T) + \frac{1}{2}a(3T)^2 \\ \end{aligned}$

Let $a$ be the subject,

$\begin{aligned} a & = \frac{8}{T^2} - \frac{2u}{T} \\ a & = \frac{6}{T^2} - \frac{u}{T} \\ a & = \frac{16}{3T^2} - \frac{2u}{3T} \end{aligned}$

As is known $T=0.2$ ,

$\begin{aligned} a & = 200- 10u \\ a & = 150 - 5u\\ a & = \frac{400}{3} - \frac{10u}{3} \end{aligned}$

Solving,

$u=10\enspace (\mathrm{cm\, s^{-1}})$ and $a=100\enspace (\mathrm{cm})$ .

And the answer is D.

Roughwork.

Unnecessarily tedious,

,

be simple.

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29	30	31

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