6) A windsurfer who is surfing on a small lake decides to sail directly out from shore. The distance from shore, $d$, in metres at time $t$ seconds is represented by the function $d(t)=0.002 t^{3}-0.1 t^{2}+3 t, 0 \leq t$
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a) Find the windsurfer's average speed during the first four seconds.
[2 marks]

Answer

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Answer

Calculate the average speed: $\frac{16}{4}$=$\boxed{4}$

Steps

Step 1 ：Find the distance at time t=0: d(0)=0.002(0)^3-0.1(0)^2+3(0)=0

Step 2 ：Find the distance at time t=4: d(4)=0.002(4)^3-0.1(4)^2+3(4)=16

Step 3 ：Calculate the total distance traveled: 16-0=16

Step 4 ：Calculate the average speed: $\frac{16}{4}$=$\boxed{4}$