An object is moving along a straight line in such a way that after t minutes, its speed is $v ( t ) = 4 t ^ { 2 } + 3 t + 1$ meters per minute. How far does the object travel during the 3rd minute?
A) $\frac { 203 } { 6 }$ meters
B) $\frac { 205 } { 6 }$ meters
C) $\frac { 209 } { 6 }$ meters
D) $\frac { 211 } { 6 }$ meters

Question

Quizplus · Accepted Answer

The distance traveled during the 3rd minute is the integral of the velocity function from t = 2 to t = 3:$$\int_2^3 (4t^2 + 3t + 1) dt = \left[\frac{4}{3}t^3 + \frac{3}{2}t^2 + t\right]_2^3 = \frac{203}{6}$$

An Object Is Moving Along a Straight Line in Such v(t)=4t2+3t+1v ( t ) = 4 t ^ { 2 } + 3 t + 1v(t)=4t2+3t+1

An Object Is Moving Along a Straight Line in Such $v ( t ) = 4 t ^ { 2 } + 3 t + 1$