Title: Approximating Instantaneous Rates of Change Pre-Video Questions
Course: Calculus Videos Project > Section: Approximating Instantaneous Rate of Change

Q: 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?
- meters per second
- meters per second
- meters per second
- meters per second
- meters per second
- meters per second
- Take the average of b. and c.
A: meters per second

Q: 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

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.
A: Because the car’s speed is always increasing, an average speed over an interval of time prior to 5 seconds must be an underestimate.

Q: 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

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).
A: Use a smaller time interval (which might require additional data).