Given $\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8$ , find S if the initial velocity is 10 m/sec upward and the initial position is 5 m above the ground.
A) $S = - 4.9 t ^ { 2 } + 10 t + 5$
B) $S = 4.9 t ^ { 2 } + 10 t + 5$
C) $S = - 9.8 t ^ { 2 } + 10 t + 5$
D) $S = 9.8 t ^ { 2 } + 10 t + 5$

Question

Quizplus · Accepted Answer

The given second derivative $\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8$ represents the acceleration due to gravity acting downward. Integrating this once gives the velocity function $v(t) = -9.8t + C_1$, where $C_1$ is the initial velocity, which is given as 10 m/s upward. Integrating again gives the position function $s(t) = -4.9t^2 + 10t + C_2$, where $C_2$ is the initial position, given as 5 m. Therefore, the correct equation for $S$ is $S = - 4.9 t ^ { 2 } + 10 t + 5$.

Given d2sdt2=−9.8\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8dt2d2s​=−9.8

Given $\frac { d ^ { 2 } s } { d t ^ { 2 } } = - 9.8$