本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
A physicist is studying the motion of two separate /7q mwz4r:ifptb*ms6-ym*fu particles moqggmnib,m1e x/yt ir(.;t7hv 4wg6 *xving in a straight line. She measures the d , qxt/igmvbh.g7x*(m4;6wirn ge1ty isplacement 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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