The velocity of a particle moving along a line is $t ^ { 3 } - t$ meters per second. Find the distance traveled in meters during the time interval $0 \leq t \leq 2$ .
A) $\frac { 7 } { 4 }$

B) $\frac { 4 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 3 } { 4 }$
E) $\frac { 3 } { 2 }$
F)$\frac { 2 } { 5 }$

G) $\frac { 5 } { 2 }$

H0 $\frac { 9 } { 4 }$

Question

The velocity of a particle moving along a line is $t ^ { 3 } - t$ meters per second. Find the distance traveled in meters during the time interval $0 \leq t \leq 2$ .
A) $\frac { 7 } { 4 }$ 
 
B) $\frac { 4 } { 3 }$ 
C) $\frac { 2 } { 3 }$
D) $\frac { 3 } { 4 }$ 
E) $\frac { 3 } { 2 }$
F)$\frac { 2 } { 5 }$

G) $\frac { 5 } { 2 }$

H0 $\frac { 9 } { 4 }$

Quizplus · Accepted Answer

To find the distance traveled, integrate the velocity function $t^3 - t$ from 0 to 2. The integral is $\int_0^2 (t^3 - t) \, dt = \left[\frac{t^4}{4} - \frac{t^2}{2}\right]_0^2 = \left(\frac{16}{4} - \frac{4}{2}\right) - (0) = 4 - 2 = 2$. The distance is 2 meters.

The Velocity of a Particle Moving Along a Line Is t3−tt ^ { 3 } - tt3−t

The Velocity of a Particle Moving Along a Line Is $t ^ { 3 } - t$