Solve the problem.
-Given the velocity and initial position of a body moving along a coordinate line at time t, ﬁnd the body's position at time t.
V = -14t + 6, s(0) = 10
A) $\mathrm { s } = 7 \mathrm { t } ^ { 2 } + 6 \mathrm { t } - 10$
B) $s = - 7 t ^ { 2 } + 6 t - 10$
C) $s = - 14 t ^ { 2 } + 6 t + 10$
D) $s = - 7 t ^ { 2 } + 6 t + 10$

Question

Solve the problem.
-Given the velocity and initial position of a body moving along a coordinate line at time t, ﬁnd the body's position at time t.
V = -14t + 6, s(0) = 10 
A) $\mathrm { s } = 7 \mathrm { t } ^ { 2 } + 6 \mathrm { t } - 10$
B) $s = - 7 t ^ { 2 } + 6 t - 10$
C) $s = - 14 t ^ { 2 } + 6 t + 10$
D) $s = - 7 t ^ { 2 } + 6 t + 10$

Quizplus · Accepted Answer

Integrate the velocity function to get the position function: 
$$s(t)=-7t^2+6t+C$$
Use the initial position $s(0)=10$ to solve for the constant $C$:
$$s(0)=-7(0)^2+6(0)+C=10$$
$$C=10$$
Substitute $C=10$ back into the position function: 
$$s(t)=-7t^2+6t+10$$
Therefore, the answer is choice D.

Solve the Problem s=7t2+6t−10\mathrm { s } = 7 \mathrm { t } ^ { 2 } + 6 \mathrm { t } - 10s=7t2+6t−10

Solve the Problem $\mathrm { s } = 7 \mathrm { t } ^ { 2 } + 6 \mathrm { t } - 10$