A roller coaster in the figure below starts at the top of a straight track is inclined 30° with the horizontal. this causes it to accelerate at a rate of 4.9 m/s^2 (1/2g). What is the roller coasters speed after 5s? How far does it travel during that time?

-2/

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for