The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35 s^-1)t]. At what value of t after t = 0 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

Given equation: x = (12.4 cm) cos[(6.35 s^-1)t]

We are looking for the time at which x = 8.47 cm.

So we need to solve:

8.47 cm = (12.4 cm) cos[(6.35 s^-1)t]

cos[(6.35 s^-1)t] = 8.47/12.4 = 0.6831

Using inverse cosine function, we get:

(6.35 s^-1)t = cos^-1(0.6831)

t = cos^-1(0.6831) / 6.35 s^-1

t = 0.1288 s

Therefore, the cart will first be located at x = 8.47 cm after t = 0.1288 s.

The closest answer choice is C) 0.129 s.

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