find the body's position at time t a=10cos 5t, v (0)= 10,s (0)=10
Mathematics
jchapman
Question
find the body's position at time t a=10cos 5t, v (0)= 10,s (0)=10
1 Answer

1. User Answers LammettHash
[tex]a(t)=10\cos5t[/tex]
[tex]v(t)=\displaystyle\int 10\cos5t\,\mathrm dt=2\sin5t+C_1[/tex]
Since [tex]v(0)=10[/tex], you have
[tex]10=2\sin0+C_1\implies C_1=10[/tex]
so
[tex]v(t)=2\sin5t10[/tex]
Next,
[tex]s(t)=\displaystyle\int(2\sin5t10)\,\mathrm dt=\dfrac25\cos5t10t+C_2[/tex]
Since [tex]s(0)=10[/tex], you get
[tex]10=\dfrac25\cos010\times0+C_2\implies C_2=\dfrac{52}5[/tex]
and so
[tex]s(t)=\dfrac25\cos5t10t+\dfrac{52}5[/tex]