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14.04.2020 •
Mathematics
At tequals0, a train approaching a station begins decelerating from a speed of 160 mi/hr according to the acceleration function a(t)equalsnegative 1280 (1 plus 4 t )Superscript negative 3 mi/hrsquared, where tgreater than or equals0. How far does the train travel between tequals0 and tequals0.2? Between tequals0.2 and tequals0.4?
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Ответ:
The distance the train travels between 0 and 0.2 hours is 17.78 miles
The distance the train travels between 0.2 and 0.4 hours is 6.8376 miles
Step-by-step explanation:
v₁ = 160 mi/hr at t = 0
Deceleration a = 1280 ( 1+ 4t)^(-3)
The velocity at a future time is given by
Therefore, plugging the values we get
Which gives
Similarly, the position of the vehicle is given by
Which gives s(0) = 0 and![v(t) =160(1+4t)^{-2}](/tpl/images/0599/6273/e2ba4.png)
Therefore,
Which gives
Therefore, the distance traveled between points 0 and 0.2 is given by
Similarly the distance the train travels between 0.2 and 0.4 seconds is
Ответ:
Remember this, always translate before you dilate. Also, you would want to translate to the left, not to the right, so by process of elimination I came up with this answer,