Solve the problem.
-Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, ﬁnd the body's position at time t.
A = 20, v(0) = -13, s(0) = 8
A) $s = 10 t ^ { 2 } - 13 t + 8$
B) $s = 10 t ^ { 2 } - 13 t$
C) $s = 20 t ^ { 2 } - 13 t + 8$
D) $s = - 10 t ^ { 2 } + 13 t + 8$

Question

Solve the problem.
-Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, ﬁnd the body's position at time t.
A = 20, v(0) = -13, s(0) = 8 
A) $s = 10 t ^ { 2 } - 13 t + 8$
B) $s = 10 t ^ { 2 } - 13 t$
C) $s = 20 t ^ { 2 } - 13 t + 8$
D) $s = - 10 t ^ { 2 } + 13 t + 8$

Quizplus · Accepted Answer

The position $s$ at time $t$ can be found by integrating the acceleration $A$ to get the velocity, and then integrating the velocity to get the position. Given $A = 20$, the integral of acceleration with respect to $t$ gives the velocity function $v(t) = 20t + C$, where $C$ is the initial velocity $v(0) = -13$. Integrating the velocity function gives the position function $s(t) = 10t^2 - 13t + C'$, where $C'$ is the initial position $s(0) = 8$. Therefore, the position function is $s = 10t^2 - 13t + 8$.

Solve the Problem s=10t2−13t+8s = 10 t ^ { 2 } - 13 t + 8s=10t2−13t+8

Solve the Problem $s = 10 t ^ { 2 } - 13 t + 8$