Solve the problem.
-Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time $t$, finc body's position at time $t$.
$\mathrm { a } = 9.8 , \mathrm { v } ( 0 ) = 4 , \mathrm {~s} ( 0 ) = 13$
A) $s = 9.8 \mathrm { t } ^ { 2 } + 4 \mathrm { t } + 13$
B) $\mathrm { s } = 4.9 \mathrm { t } ^ { 2 } + 4 \mathrm { t } + 13$
C) $s = - 4.9 t ^ { 2 } - 4 t + 13$
D) $s = 4.9 t ^ { 2 } + 4 t$ the

Question

Solve the problem.
-Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time $t$, finc body's position at time $t$. 
$\mathrm { a } = 9.8 , \mathrm { v } ( 0 ) = 4 , \mathrm {~s} ( 0 ) = 13$
A) $s = 9.8 \mathrm { t } ^ { 2 } + 4 \mathrm { t } + 13$
B) $\mathrm { s } = 4.9 \mathrm { t } ^ { 2 } + 4 \mathrm { t } + 13$
C) $s = - 4.9 t ^ { 2 } - 4 t + 13$
D) $s = 4.9 t ^ { 2 } + 4 t$ the

Quizplus · Accepted Answer

We know that acceleration is the second derivative of position with respect to time. Integrating the acceleration gives us the velocity, and integrating the velocity gives us the position. Integrating the given acceleration of 9.8 gives us a velocity of 9.8t + 4 (adding the constant of integration, which is the initial velocity of 4). Integrating the velocity of 9.8t + 4 gives us a position of 4.9t^2 + 4t + 13 (adding the constant of integration, which is the initial position of 13). Therefore, the correct choice is B.

Solve the Problem ttt , Finc Body's Position at Time ttt a=9.8,v(0)=4, s(0)=13\mathrm { a } = 9.8 , \mathrm { v } ( 0 ) = 4 , \mathrm {~s} ( 0 ) = 13a=9.8,v(0)=4, s(0)=13

Solve the Problem $t$ , Finc Body's Position at Time $t$ $\mathrm { a } = 9.8 , \mathrm { v } ( 0 ) = 4 , \mathrm {~s} ( 0 ) = 13$