The position of a cat running from a dog down a dark alley is given by the values of the table.t(seconds)012345s(feet)020306990107 Draw the graph of the function for yourself and estimate the instantaneous velocity of the cat (ft/sec) when t=2

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The position of a cat running from a dog down a dark alley is given by the values of the table.t(seconds)012345s(feet)020306990107 Draw the graph of the function for yourself and estimate the instantaneous velocity of the cat (ft/sec) when t=2
The position of a cat running from a dog down a dark alley is given by the values of the table.
t(seconds)012345s(feet)020306990107

 
 Draw the graph of the function for yourself and estimate the instantaneous velocity of the cat (ft/sec) when t=2 

The position of a cat running from a dog down a dark alley is given by the values of the table.t(seconds)012345s(feet)020306990107 Draw the graph of the function for yourself and estimate the instantaneous velocity of the cat (ft/sec) when t=2
Answer:The instantaneous velocity of the cat is 20 ft/sec when t=2.
【解析】按照表格数据,很明显猫咪是在做变速运动,小狗所在的位置为起点,昏暗的巷子为跑道.则按照物理学公式,t=1~5时,对应的加速度分别用a1~a5表示,对应的瞬时速度分别用v1～v5表示,位移s分别用s1～s5表示；t=0时,初速度用V0表示；此外,Δt表示时间差.
【解】依题意,当t=0时,s=0,所以有初速度v0=0；
t=1时,s1=v0×Δt+（1/2）×a1×Δt=0×（1-0）+（1/2）×a1×（1-0）=（1/2）×a1=20,解得a1=40（ft/sec）
所以v1=v0+a1×Δt=0+40×（1-0）=40（ft/sec）；
t=2时,s2=v1×Δt+（1/2）×a2×Δt=40×（2-1）+（1/2）×a2×（2-1）=40+（1/2）×a2=30,解得a2=-10（ft/sec）
所以v2=v1+a2×Δt=40+（-10）×（2-1）=20（ft/sec）
答：t=2sec时,对应的瞬时速度为20 ft/sec.
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