本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
A physicist is studying the mot beaw mx5d.0w7ion of two separate particles mo9 dgx6/3y*,l6oyhtoz w9vu qjving in a straight line. She measures d9g y6v*ty /3o69 qjzlw,hux othe displacement of each particle from a fixed origin over the course of 10 seconds The physicist found that the displacement of particle A, $s_{A} \mathrm{~cm}$ , at time t seconds can be modelled by the function $s_{A}(t)=7 t+9$ , where $ 0 \leq t \leq 10$ .
The physicist found that the displacement of particle B,$s_{B} \mathrm{~cm}$ , at time t seconds can be modelled by the function $s_{B}(t)=\cos (3 t+5)+8 t+4 $.
1. Use the physicist's models to find the initial displacement of
1. Particle A ;
2. Particle B correct to three significant figures.
2. Find the values of t when $s_{A}(t)=s_{B}(t)$ .
3. For t>6 , prove that particle B was always further away from the fixed origin than particle A .
4. For $ 0 \leq t \leq 10$ , find the total amount of time that the velocity of particle A was greater than the velocity of particle B .
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