Question

select the realistic problem for which these are the correct equations. be sure that the answer your problem requests is consistent with the equation given. a 1000 kg race car enters a 25 m radius curve and accelerates around the curve for 10.0 s. the forward force provided by the cars wheels is 1500 n. after 10.0 s the car has moved 125 m around the track. find the initial and final angular velocities. a 1000 kg race car enters a 50 m radius curve and accelerates around the curve for 10.0 s. the forward force provided by the cars wheels is 1500 n. after 10.0 s the car has moved 125 m around the track. find the initial and final angular velocities. a 1000 kg race car enters a 25 m radius curve and accelerates around the curve for 15.0 s. the forward force provided by the cars wheels is 1500 n. after 15.0 s the car has moved 125 m around the track. find the initial and final angular velocities. a 1000 kg race car enters a 50 m radius curve and accelerates around the curve for 15.0 s. the forward force provided by the cars wheels is 1500 n. after 15.0 s the car has moved 125 m around the track. find the initial and final angular velocities. part b finish the solution of the problem. express your answer in radians per second. ωf = incorrect; try again previous answers request answer submit ωf=ωi+((1.5 m/s²)/(50 m))(10 s)+((1.5 m/s²)²/2(50 m))(10 s)² 2.5 rad = 0 rad+ωi(10 s)+((1.5 m/s²)/(50 m))(10 s)

Explanation:

Step1: Identify the relevant kinematic - angular motion formula

The formula for angular velocity in non - uniform circular motion is $\omega_f=\omega_i+\alpha t+\frac{1}{2}\alpha t^2$, but we can also use the relationship between linear and angular motion. The linear displacement $s = r\theta$, and the average angular velocity $\bar{\omega}=\frac{\theta}{t}$. First, we find the angular displacement $\theta=\frac{s}{r}$. Here, $s = 125\ m$ and $r = 50\ m$, so $\theta=\frac{125}{50}=2.5\ rad$.

Step2: Assume initial angular velocity $\omega_i = 0$ (not given otherwise)

We know that the average angular velocity $\bar{\omega}=\frac{\theta}{t}$, and if the motion is uniformly accelerated from rest, the final angular velocity $\omega_f$ can be related to the average angular velocity. For uniformly accelerated motion from rest, $\bar{\omega}=\frac{\omega_i+\omega_f}{2}$. Since $\omega_i = 0$, $\bar{\omega}=\frac{\omega_f}{2}$. And $\bar{\omega}=\frac{\theta}{t}$, where $t = 10\ s$ and $\theta = 2.5\ rad$. So $\bar{\omega}=\frac{2.5}{10}=0.25\ rad/s$. Then $\omega_f = 2\bar{\omega}$.

Step3: Calculate the final angular velocity

$\omega_f=2\times0.25 = 0.5\ rad/s$

Answer:

$0.5\ rad/s$