Question

evaluate

Answer 1

s(0) = 480
s'(0) = 64
\[s''(t) = -32\]
\[s'(t)=\int\limits\limits s''(t)dt=-32\int\limits dt = -32t+C_1\]
\[s'(0)=-32(0)+C_1=64 \rightarrow C_1=64\]
\[s'(t) = -32t + 64\]
\[s(t) = \int\limits s'(t) = (-32t-64)dt=-32 \int\limits tdt + \int\limits 64dt=-16t^2+64t+C_2\]
\[s(0) = -16(0)^2 + 64(0) + C_2 = 480 \rightarrow C_2 = 480\]
\[s(t) = -16t^2 + 64t + 480\]
\[s(t) = -16t^2 +64t + 480 = 0 \rightarrow t ≅ 7.8310\]
\[s'(7.8310) ≅ -32t+480 ≅ -250.592 \frac{ ft }{ \sec }\]