一物体从静止开始,以加速度a做匀加速直线运动,接着以a′做匀减

一物体从静止开始,以加速度a做匀加速直线运动,接着以a′做匀减速直线运动,直至停止.试证明物体走完全程s所花的时间为t=.

答案

证明:设物体做匀加速运动的时间为t1,位移为s1,做匀减速运动的时间为t2,位移为s2.物体做加速运动的末速度,即物体做减速运动的初速度为v0,则物体走完全程所用的总时间为

t=t1+t2=+=+=

    得v=

    物体的总位移为

s=s1+s2=+=(+)

    得t=

命题由此得证.

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