The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm)cos[(6.35 s^-1)t].At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm? A)4.34 s B)0.108 s C)0.129 s D)7.39 s E)7.75 s

Question

Quizplus · Accepted Answer

To find the time when the cart is first located at x=8.47 cm, we need to solve for t in the given equation x = (12.4 cm)cos[(6.35 s^-1)t] = 8.47 cm
cos[(6.35 s^-1)t] = 8.47 cm / (12.4 cm) = 0.683
Taking the inverse cosine of both sides, we have:
(6.35 s^-1)t = cos^-1(0.683) = 0.819 radians
t = 0.819 radians / (6.35 s^-1) = 0.129 s
Therefore, the answer is (C) 0.129 s.

The Position of an Air-Track Cart That Is Oscillating on a Spring