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A car speeds up as it drives away from a traffic light. The car’s GPS unit records its distance from the light in the table below:

 Time (seconds) Distance (meters) 0 0 1 1 2 3 3 6 4 10 5 15 6 21 7 27

Using only the data from the table, what method could you use to find the best possible underestimate to the car’s speed at the 5-second mark?
(a)  $\dfrac {15}{5}=3$ meters per second (b)  $\dfrac {15-10}{5-4}=5$ meters per second (c)  $\dfrac {21-15}{6-5}=6$ meters per second (d)  $\dfrac {21-10}{6-4}=5.5$ meters per second (e) $\dfrac {15+10}{2} = 12.5$ meters per second (f) $\dfrac {21+15}{2} = 18$ meters per second Take the average of (b) and (c)
Which statement below best explains why the value you found underestimates the car’s speed at 5 seconds.
Because I used a time less than 5 seconds. Because I used a time greater than 5 seconds. Because I used an interval of time that includes 5 seconds. Because the value I got for meters per second would be less than all other values for meters per second. Because the car’s speed is always increasing, an average speed over an interval of time prior to 5 seconds must be an underestimate. Because the car’s speed is always increasing, an average speed over an interval of time after 5 seconds must be an underestimate.
What additional information might you need to improve your underestimate to the car’s speed at the 5-second mark?
I do not need to make an improvement because the speed I calculated is the car’s speed at the 5-second mark. Use a different pair of points from the table to underestimate the speed. Use two pairs of points from the table to compute two speeds, then average these speeds. Use a larger interval of time (e.g., if I originally used a 1-second time interval, a 2-second time interval would improve my approximation). Use a smaller time interval (which might require additional data).