"The function x = (2.5 m) cos[(4π rad/s)t + π/2 rad] gives the simple harmonic motion of a body. Find the following values at t = 5.0 s. "
(a) the displacement m
(b) the velocity (Include the sign of the value in your answer.) m/s
(c) the acceleration (Include the sign of the value in your answer.) m/s2
(d) the phase of the motion rad
(e) the frequency of the motion Hz
(f) the period of the motion
I tried:
3.14 / 2 = 1.57
Then, 4 * 3.14 = 12.56. Then, 12.6*5 = 62.8
Add both: 64.4
Apply cos in rad = 0.002
Times 2.5 = 0.08160899570341
But it says that's wrong. Am I missing something??
The error comes from the fact that you have used the approximation $\pi \approx 3.14$ in your intermediate calculations. The rounding error is causing an error in the final answer. You can do this problem fairly easily without rounding.
$$ \cos\left (4\pi\cdot5 + \frac{\pi}{2} \right) = \cos\left (\frac{41\pi}{2} \right) = \cos\left (\frac{\pi}{2} \right) $$
Can you take it from here?