本题目来源于试卷: Kinematics，类别为 IB数学
[问答题]
A particle moves bac; hqf/mpd sj,uv-qs ,ezyx/ -7qd/eba2thzsq;,a:bey+b . * jk and forth in a straight line. Its velocity $ v \mathrm{~m} \mathrm{~s}^{-1}$ at time t seconds is given by
$v=3 t-\frac{3}{4} t^{2}, \quad 0 \leq t \leq 7$ .
At time t=0 , the displacement s of the particle from the starting point is 1 m .
1. Find the displacement of the particle when t=5 .
2. Sketch a displacement/time graph for the particle, $0 \leq t \leq 7$ , showing clearly where the curve meets the axes and the coordinates of the points where the displacement takes the greatest and least values.
For t>7 , the displacement of the particle is given by
$s=\alpha+\beta \cos \left(\frac{2 \pi t}{7}\right)$
such that s is continuous for all $t \geq 0$ .
3. Given that s=9 when t=10.5 , find the values of $\alpha and \beta$ .
4. Find the times $t_{1}$ and $ t_{2}\left(0
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