At time t seconds, the center of a bobbing cork is y=4sint centimeters above (or below) water level.
What is the velocity of the cork at t = 0, π/2, π
just kidding, I figured it out! It's -4, 0, and 4
velocity=p'=4cost
at t=0, v=4
at t=PI/2, v=0
at t=PI, -4
To find the velocity of the cork at different times, we need to take the derivative of the position function with respect to time.
Given that the position of the cork is y = 4sin(t) centimeters, we can take the derivative of this function to find the velocity.
The derivative of sin(t) with respect to t is cos(t), so the derivative of 4sin(t) would be 4cos(t).
Now, let's find the velocity at the given times:
1. At t = 0:
Substituting t = 0 into the derivative function, we get v = 4cos(0) = 4(1) = 4 centimeters per second. So, the velocity of the cork at t = 0 is 4 cm/s.
2. At t = π/2:
Substituting t = π/2 into the derivative function, we get v = 4cos(π/2) = 4(0) = 0 centimeters per second. So, the velocity of the cork at t = π/2 is 0 cm/s.
3. At t = π:
Substituting t = π into the derivative function, we get v = 4cos(π) = 4(-1) = -4 centimeters per second. So, the velocity of the cork at t = π is -4 cm/s.
Therefore, the velocities of the cork at t = 0, π/2, and π are 4 cm/s, 0 cm/s, and -4 cm/s, respectively.