Question

A roller coaster accelerates from a stop. Table 1 is represented by a quadratic function
f
(
t
)
, where
f
(
t
)
is the distance the roller coaster has traveled, in feet, based on the time,
t
, in seconds, since it started moving.

At the end of the ride, the same roller coaster begins to slow down as it approaches the station. Table 2 is represented by a quadratic function
g
(
s
)
, where
g
(
s
)
is the safe stopping distance, in feet, based on the speed,
s
, in miles per hour the roller coaster is traveling.

image
Which function represents the distance traveled by the roller coaster over time?



A.
f
(
t
)
=
10
t
2

B.
f
(
t
)
=
20
t
2

C.
f
(
t
)
=
5
t
2
+
5
t

D.
f
(
t
)
=
20
t
2
−
10
t

Answer 1

Answer: A

Reason: Starting from a stop means initial velocity = 0, so f has no linear term and is of the form f(t)=k t^2. Using the table value f(1)=10 (from Table 1) gives k=10, so f(t)=10t^2.