有个关于求导问题的引申数学题,YesterdayIgotintoanargumentwithmyboyfriendoveraquestiononvelocityandacceleration,andIamhopingyoucansettleitforus.Webothagreethattheaccelerationofanobjectattimetisjustthe

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有个关于求导问题的引申数学题,
Yesterday I got into an argument with my boyfriend over a question on velocity and acceleration,and I am hoping you can settle it for us.
We both agree that the acceleration of an object at time t is just the rate of change of its velocity at that moment (in other words,if the velocity is given by v(t),the acceleration is a(t) = v’(t)).But here is where we argued:my boyfriend says that if the velocity of an object at time t is 0,its acceleration at that moment is also 0.I said no,even if the velocity at that moment is 0 it could be changing,so the acceleration would reflect that change and be different than 0.
He said I was ridiculous,if the velocity is zero the object is not moving so its acceleration is also zero.So I got mad and said you are the ridiculous one,zero acceleration just means there is no change in velocity.Imagine you are driving and you slow down at an intersection then speed up again:you could see the needle on your speedometer hit 0 in between,meaning your velocity at that moment was zero,but your speed was changing all along so you acceleration was definitely not zero!
By this time we were both pretty irritated so we dropped the subject… but he says my explanation is mathematically impossible.I am sure there is a mathematical proof but do not know how to write it!Who is right?If I am correct,could you please provide an example of a velocity function v(t) where v(t1) = 0 but the acceleration v’(t1) ≠
大概意思就是 当速度为0的时候,加速度不一定为0.这句话 怎么用V（t）和V‘（t）来证明它是正确的?

Answer 1

可能不太严谨,根据导数的定义也许行.设当t=t(0)时,v(t0)=0,v'(t0)=lim(t~t0)(v(t)-v(t0))/(t-t0)=lim(t~t0)v(t)/(t-t0),因为v(t)不一定等于0,所以v'(t0)不一定等于0