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Now velocity can be found by calculating the area under the slope. But that turns out to be 0, which is weird. It’s probably because I haven’t understood reading the graphs yet. It’s a simple question, but I still need help solving it.

$$Area=8-8=0$$ Which is obviously wrong. How should I do this?

Aditya
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2 Answers2

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The elevator accelerates from rest at $2$ m/s$^2$ for $4$ seconds so it will reach a velocity of $2\cdot4 = 8$ m/s. It then continues at $8$ m/s for $4$ seconds, then decelerates at $-2$ m/s$^2$ for $4$ seconds back to zero velocity.

To get the distance traveled (height), as the acceleration is uniform, it's the average velocity of each segment times the time. This will be $4\cdot 4 + 8\cdot 4 + 4\cdot 4 = 64$ m.

Phil H
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Draw velocity and time graph , area will give you height. it will be v=2t ,v=8 , v=-2t respectively for your intervals it's a trapezoid of height 8 . you can take it from here

Rishi
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  • Is it possible to do it without drawing a graph? – Aditya Sep 05 '19 at 12:24
  • @Aditya Sure, you can also calculate the integral $\int_{t=0}^{12}v(t),dt.$ Or make intellligent reasoning about the average speeds in the three intervals. I would think drawing the graph is easier. – Jyrki Lahtonen Sep 05 '19 at 12:26
  • It is easy with graph , Use $s=ut+\frac{1}{2}at^2$ if you want or do it by integral way – Rishi Sep 05 '19 at 12:27