Question

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 = sin 2t + 10, v(0) = - 12 , s(0) = -4

Answer 1

\[
v(t) = -\frac 1 2 \cos(2t) + 10 t + c\\
v(0) =12= -\frac 1 2 + c
\\
c= \frac {25}2\\

v(t) = -\frac 1 2 \cos(2t) + 10 t + \frac {25}2\\

s(t) = -\frac 1 4 \sin(2t) + 5 t^2 + \frac {25}2 t + b\\
s(0)= -4 = b\\\
s(t) = -\frac 1 4 \sin(2t) + 5 t^2 + \frac {25}2 t -4\\
\]