Solve the problem.
-An object is rolling with a driving force that suddenly ceases. The object then rolls 10 meters in the first second, and in each subsequent interval of time it rolls 80% of the distance it had rolled the second before. This slowing
Is due to friction. How far will the object eventually roll?
A) It will roll an infinite distance.
B) 20.0 m
C) 12.2 m
D) 50.0 m

Question

Quizplus · Accepted Answer

The object's rolling distance forms a geometric series with the first term $a = 10$ meters and a common ratio $r = 0.8$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $S$ is the total distance. Substituting the given values, $S = \frac{10}{1 - 0.8} = \frac{10}{0.2} = 50$ meters.

Solve the Problem. -An Object Is Rolling with a Driving Force That Suddenly