甲乙两车的距离为:26-(15t-1/2×0.5t^2)+10t=26-15t+1/4t^2+10t
=1/4t^2-5t+26=1/4(t-10)^2-25+26
由此得知,两车不能相撞,且当t=10s时有最小距离,最小距离为1m
扩展1:当两车原来的距离应该25时,甲车恰好撞不上乙车.
扩展2:将式子中的26换成24则两车的距离为:1/4(t-10)^2-1
1/4(t-10)^2-1=0 推出t=12s或者8s,12s排除,t=8s
扩展3:有两个解是因为假设两车不是相撞而是甲车从乙车旁边开过,由于甲车在减速,12s之后乙车会再次超过甲车.
扩展4:甲乙两车的距离为:64-(15t-1/2×0.5t^2)+5t=64-15t+1/4t^2+5t
=1/4t^2-10t+64
1/4t^2-10t+64=0
t^2-40t+256=0
(t-20)^2-144=0
t-20=12或-12
t=32s或8s
能相遇两次,在8s和32s时相遇