A race car is traveling on a straight track at a velocity of 80 meters per second when the brakes are applied at time $t = 0$ seconds. From time $t = 0$ to the moment the race car stops, the acceleration of the race car is given by $a ( t ) = - 6 t ^ { 2 } - t$ meters per second per second. During this time period, how far does the race car travel?
(A) 188.229 m
(B) 198.766 m
(C) 260.042 m
(D) 267.089 m

A particle moves along the $x$-axis. The velocity of the particle at time $t$ is $6 t - t ^ { 2 }$. What is the total distance traveled by the particle from time $t = 0$ to $t = 3$ ?
(A) 3
(B) 6
(C) 9
(D) 18
(E) 27

The graph above gives the velocity, $v$, in ft/sec, of a car for $0 \leq t \leq 8$, where $t$ is the time in seconds. Of the following, which is the best estimate of the distance traveled by the car from $t = 0$ until the car comes to a complete stop?
(A) 21 ft
(B) 26 ft
(C) 180 ft
(D) 210 ft
(E) 260 ft

The velocity $v ( t )$ at time $t ( t \geq 0 )$ of a point P moving on a number line is $$v ( t ) = - 2 t + 4$$ What is the distance traveled by point P from $t = 0$ to $t = 4$? [3 points]
(1) 8
(2) 9
(3) 10
(4) 11
(5) 12

The velocity $v ( t )$ of a point P moving on a number line at time $t ( t \geq 0 )$ is $$v ( t ) = 2 t - 6$$ If the distance traveled by point P from time $t = 3$ to time $t = k$ ($k > 3$) is 25, what is the value of the constant $k$? [4 points]
(1) 6
(2) 7
(3) 8
(4) 9
(5) 10

The velocity $v ( t )$ and acceleration $a ( t )$ of a point P moving on a number line at time $t$ ($t \geq 0$) satisfy the following conditions. (가) When $0 \leq t \leq 2$, $v ( t ) = 2 t ^ { 3 } - 8 t$. (나) When $t \geq 2$, $a ( t ) = 6 t + 4$.
Find the distance traveled by point P from time $t = 0$ to $t = 3$. [4 points]