Answer:
s = 6 m
Step-by-step explanation:
The value of the velocity v is given as:
[tex]v = \frac{ds}{dt} = 6 sin(2t)[/tex] m/s
To find s, we have to integrate and apply the initial values of s = o when t = 0:
[tex]\frac{ds}{dt} = 6 sin(2t)\\\\\int\limits^s_0 {ds} = \int\limits^t_0 {6sin(2t)} \, dt\\\\s|^s_o = -3cos(2t)|^t_o\\\\s - 0 = -3cos(2t) -(-3cos(0))\\\\s = -3cos(2t) + 3(1)\\\\s = -3cos(2t) + 3[/tex]
When t = π/2, s will be:
s = -3cos(2 * π/2) + 3
s = -3cos(π) + 3
s = -3(-1) + 3
s = 3 + 3
s = 6 m
