匿名
匿名 發問於 科學及數學其他 - 科學 · 10 年前

加速度的意義

我想搞清一d概念

以前我以為,加速度等於:

例如車子從靜止狀態加速,行走了3秒,加速度為2m s^-2

我以為,車子在三秒內,共走了2+4+6=14m

現在當然知道全錯

但我想問,點解會咁怪

從方程中計,車子3秒內應該共行了ut+1/2 at^2=9m

從t=0開始加速,t=1時,車子唔係行左兩米,反而係1m,即係加速度既一半!!

why?點解加速度既意義

唔係t=1時,車子行左2m

t=2時,行多4m

t=3時,行多6m

總共14m??

更新:

1.If say that acceleration is the "rate of change of velocity" then why the is m/s^2 instead of % to be the the system of unit.I dont get it.

You say "Thus, it is clear that in the first second, the velocity has increased by 2 m/s. It doesn't mean that the velocity is 2 m/s."

更新 2:

oh...

another question

by 1s,the final v=2m/s

but why dont it mean the car running 4m during 1s-2s??

1 個解答

評分
  • 天同
    Lv 7
    10 年前
    最愛解答

    You have got a wrong interpretation on "acceleration". Acceleration is the rate of change of velocity. An acceleration of, say 2 m/s^2, means that the velocity will increase by 2 m/s for every 1 s time interval. Notice that it refers to the "increase" in velocity.

    Thus, it is clear that in the first second, the velocity has increased by 2 m/s. It doesn't mean that the velocity is 2 m/s. But you calculate the displacement using 2 m/s x 1s = 2 m, which is wrong, because you have made use of the formula: displacement = velocity x time, and thus mistakenly take the "increase in velocity" to be the "velocity".

    In fact, the 2 m/s is the final velocity, i.e. velocity at the end of the 1s interval. To calculate the displacement, you need to use the "average velocity" during this 1s time interval. The average velocity from t=0s to t = 1s is equal to (0+2)/2 m/s = 1 m/s. Hence, the displacement is 1 x 1 m = 1 m.Likewise, the average velocity during the time interval from t =1s to t=2s is (2+4)/2 m/s = 3 m/s, and the displacement = 3 x 1 m = 3 mThe average velocity from t=2s to t=3s is (4+6)/2 m/s = 5 m/s, hence displacement = 5 x 1 m = 5 m. Therefore the total displacement = (1+3+5) m = 9 m

    2010-11-28 12:44:09 補充:

    1. To specify acceleration as a constant percentage of the initial velocity would mean that the acceleration is NOT uniform over time, because the velocity at the start of each second of time interval is different....(contd)

    2010-11-28 12:51:41 補充:

    ...The use of the unit "m/s per s" is clear and striaght forward. It means an increase of so many m/s over a time interval of 1s.

    .

    2010-11-28 12:52:22 補充:

    2. If you take the 3rd time interval, you could understant the point. The velocity in this 1s interval increases from 4 to 6m/s, the change in velocity is 2 m/s, i.e. the difference in velcities....

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