Question

calculate the period (t) of uniform circular motion if the velocity is 40.0 m/s and centripetal acceleration is 20.0 m/s².
39.4 s
12.6 s
3.14 s
6.28 s

Explanation:

Step1: Encontrar el radio de la trayectoria circular

La aceleración centrípeta \(a_c=\frac{v^{2}}{r}\), despejando \(r\) se obtiene \(r = \frac{v^{2}}{a_c}\). Sustituyendo \(v = 40.0\space m/s\) y \(a_c=20.0\space m/s^{2}\):
\(r=\frac{(40.0)^{2}}{20.0}=\frac{1600}{20}=80\space m\)

Step2: Calcular el período \(T\)

La velocidad tangencial \(v=\frac{2\pi r}{T}\), despejando \(T\) se obtiene \(T=\frac{2\pi r}{v}\). Sustituyendo \(r = 80\space m\) y \(v = 40.0\space m/s\):
\(T=\frac{2\pi\times80}{40}=4\pi\approx 12.56\space s\approx12.6\space s\)

Answer:

12.6 s