Respuesta :
Answer:
1) 57 revolutions.
2) 4.52 m
3) 1531.2 m
Explanation:
Question 1:
Given:
Initial velocity, [tex]u = 0[/tex]
Final velocity, [tex]v = 19.8\ m/s[/tex]
Time, [tex]t = 7\ s[/tex]
Acceleration, [tex]a = \frac{\textrm{Final velocity-Initial velocity}}{Time}=\frac{19.8}{7}=2.83\ m/s^2[/tex]
Now, displacement of the tire is given as:
[tex]S=ut+\frac{a}{2}t^2\\S=0+\frac{2.83}{2}7^2=69.335\ m[/tex]
Displacement of tire in 1 revolution is equal to its circumference.
Therefore, displacement in 1 revolution = [tex]\pi\times(Diameter)=\pi \times 38.5\times 10^{-2}=1.2095\ m[/tex]
Now, number of revolutions is given as:
[tex]N=\frac{Total\ displacement}{Displacement\ per\ revolution}\\N=\frac{69.335}{1.2095}=57[/tex]
Therefore, the number of revolutions are 57.
Question 2:
Given:
Radius of the wheel is, [tex]R=4.8\ m[/tex]
Angle of rotation is, [tex]\theta=54[/tex]°
Converting degree to radians, we get:
[tex]\theta=54\times \frac{\pi}{180}=0.3\pi[/tex]
Now, path length is given as:
[tex]L=R\theta=(4.8)(0.3\pi)=1531.2\ m[/tex]
Therefore, the path length of a point on the wheel is 4.52 m
Question 3:
Radius of the wheel is, [tex]R=4.8\ m[/tex]
Angle of rotation is, [tex]\theta=319[/tex] radians
Now, path length is given as:
[tex]L=R\theta=(4.8)(319)=4.52\ m[/tex]
Therefore, the path length of a point on the wheel is 1531.2 m.
