# Math

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When estimating distances from a table of velocity data, it is not necessary that the time intervals are equally spaced. After a space ship is launched, the following velocity data is obtained. Use these data to estimate the height above the Earth's surface at 120 seconds.

(0,0) (5,110) (17, 374) (25,550) (44,968) (60,1320) (69,1743) (129,4563) are the data points

questions
what is the lower estimate of distance traveled
what is the upper estimate of distance traveled

• Math -

If you plot the points, it appears to be piecewise linear, with a slope change at x=60

So, interpolating between 69 and 129, we get

1743 + (51/60)(4563-1743) = 4140

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