Answer:
a)[tex]d=628.3m[/tex]
b)[tex]a_t=5m/s^2[/tex]
c)[tex]a_{cp}=10m/s^2[/tex]
Explanation:
a) If it did 10 revolutions, it returned to the original point, but it travelled 10 times the circunference [tex]C=2\pi r[/tex], where r is the radius of the circle, so we have [tex]d=10(2\pi r)=20\pi (10m)=628.3m[/tex]
b) The tangential component of this problem can be treated as a one dimensional problem, so the (tangential) acceleration [tex]a_t[/tex] needed to reach the final speed given starting from rest after traveling a distance d can be obtained using the equation for accelerated motion [tex]v^2=v_0^2+2a_td=2a_td[/tex], so we have:
[tex]a_t=\frac{v^2}{2d}=\frac{(10m/s)^2}{2(10m)}=5m/s^2[/tex]
c) We use our values in the formula for centripetal acceleration given the tangential velocity and radius:
[tex]a_{cp}=\frac{v^2}{r}=\frac{(10m/s)^2}{10m} =10m/s^2[/tex]
