Answer :
Answer:
[tex]v(t)= 30\pi cos(2\pi t)[/tex]
Step-by-step explanation:
The velocity of the particle is equal to the derivative of the displacement, so:
[tex]v(t)=s'(t)[/tex]
Now, the derivative of s(t) is equal to:
[tex]s'(t)=(2+15sin(2\pi t)'=0 + (15cos(2\pi t)*2\pi)=30\pi cos(2\pi t)[/tex]
Because we use the following properties:
If [tex]f(t) = g(t) + h(t)[/tex], then [tex]f'(t) = g'(t) + h'(t)[/tex]
If [tex]f(t) = a[/tex], where a is a constant [tex]f'(t) = 0[/tex]
If [tex]f(t) = sin(t)[/tex], then [tex]f'(t) = cos(t)[/tex]
If [tex]f(t) = sin(g(t))[/tex], then [tex]f'(t) = cos(g(t))*g'(t)[/tex]
Where f(t), g(t) and h(t) are functions of t.
So, the velocity of the particle after t seconds [tex]v(t)[/tex] is equal to:
[tex]v(t)= 30\pi cos(2\pi t)[/tex]