Home > APCALC > Chapter 3 > Lesson 3.2.1 > Problem 3-47
After completing the Ramp Lab in Chapter 2, Marquita decided to ride her bicycle down a nearby hill to gain more data on rolling objects. The data she collected is shown in the table below.
Time (sec) | ||||||
Distance (m) |
Can Marquita use this table to determine her exact velocity at
Explain. Tables only give us select values of a function. What values are we given that are close to
? Are these values close enough to find Marquita's exact velocity at ? Approximate Marquita’s velocity at
using Hana’s method. Hanna’s Method:
where represents the value whose slope you are looking for. Note: Since we do note know values that are infinitely close to
, we can find Marquita's AROC (average velocity), not her IROC (actual velocity). Marquita’s teacher observed that her data fits the function
. Assuming that her teacher is correct, compute Marquita’s exact velocities at and . Use the Power Rule to find the IROC/derivative/slope function/velocity function. Then evaluate at
and again at .