本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
A particle moves in a sag i: *4mpi(fcfyn)u:traight line and ibv u3oq1 h2 wp,m*p3klq, gi8ats velocity, v $\mathrm{~ms}^{-1} $, at time t seconds, is given by $v(t)=\left(t^{2}-2\right)^{2}$ , for $0 \leq t \leq 2 $.
1. Find the initial velocity of the particle.
2. Find the value of t for which the particle is at rest.
3. Find the total distance travelled by the particle in the first 2 seconds.
4. Show that the acceleration of the particle is given by a(t)=4 $t^{3}-8 t$ .
5. Find the values of t for which the velocity is positive and the acceleration is negative.
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