Answer:
-24.28571 rad/s²
29.57239 revolutions
3.91176 seconds
52.026478 m
Explanation:
[tex]a_t[/tex] = Tangential acceleration = -6.8 m/s²
r = Radius of wheel = 0.28
[tex]\omega_i[/tex] = Initial angular velocity = 95 rad/s
[tex]\theta[/tex] = Angle of rotation
[tex]\omega_f[/tex] = Final angular velocity
t = Time taken
Angular acceleration is given by
[tex]\alpha=\frac{a_t}{t}\\\Rightarrow \alpha=\frac{-6.8}{0.28}\\\Rightarrow \alpha=-24.28571\ rad/s^2[/tex]
The angular acceleration is -24.28571 rad/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{0^2-95^2}{2\times -24.28571}\\\Rightarrow \theta=185.80885\ rad=185.80885\times \frac{1}{2\pi}\\\Rightarrow \theta=29.57239\ rev[/tex]
The number of revolutions is 29.57239
[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow t=\frac{\omega_f-\omega_i}{\alpha}\\\Rightarrow t=\frac{0-95}{-24.28571}\\\Rightarrow t=3.91176\ s[/tex]
The time it takes for the car to stop is 3.91176 seconds
Linear distance
[tex]s=r\theta\\\Rightarrow s=0.28\times 185.80885\\\Rightarrow s=52.026478\ m[/tex]
The distance the car travels is 52.026478 m
