Question

for any time t≥0, the acceleration of a particle moving on the x-axis is a(t)=t+sin(t). At t=0. the velocity of the particle is -2. For what value t will the velocity of the particle be zero?

Answer 1

\[a(t) = \frac{ dv }{ dt }\]
thus:\[\frac{ dv }{ dt } = t + \sin t \]
\[dv = tdt + \sin(t) dt\]
Now integrate both sides

Answer 2

\[\int\limits{}dv = \int\limits{}tdt + \int\limits{}\sin(t)dt\]

Answer 3

to get velocity right