Answer:
0.033815 m/s²
12.48810875 m
Explanation:
t = Time taken = 12 s
[tex]\omega_f[/tex] = Final angular velocity = 95 rpm
[tex]\omega_i[/tex] = Initial angular velocity = 64 rpm
[tex]\alpha[/tex] = Angular acceleration
[tex]\theta[/tex] = Angle of rotation
[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\frac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\frac{95\times \frac{2\pi}{60}-64\times \frac{2\pi}{60}}{12}\\\Rightarrow \alpha=0.27052\ rad/s^2[/tex]
Tangential acceleration is given by
[tex]a_t=\alpha r\\\Rightarrow a_t=0.27052\times 0.125\\\Rightarrow a_t=0.033815\ m/s^2[/tex]
The tangential acceleration of the pedal is 0.033815 m/s²
[tex]\omega_f^2-\omega_i^2=2\alpha \theta\\\Rightarrow \theta=\frac{\omega_f^2-\omega_i^2^2}{2\alpha}\\\Rightarrow \theta=\frac{\left(95\times\frac{2\pi }{60}\right)^2-\left(64\times\frac{2\pi}{60}\right)^2}{2\times 0.27052}\\\Rightarrow \theta=99.90487\ rad[/tex]
Linear displacement would be [tex]99.90487\times \frac{1}{2\pi}\times 2\pi\times 0.125=12.48810875\ m[/tex]
Length of chain that passes in the interval is 12.48810875 m
