Hi!Need help please.
Question:A car initially traveling at 24.0 m/s undergoes a constant negative acceleration of magnitude 2.10 m/s2 after its brakes are applied.
(a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330 m?
____ rev
(b) What is the angular speed of the wheels when the car has traveled half the total distance?
___ rad/s
You know the velocity intial, the final veloctiy, and are looking for distance
Vf^2=vi^2 + 2ad
solve for d.
Then convert that to revolutions.
the average angular velocity is average velocity/circumference
To solve these problems, we need to use the equations of motion for rotational motion. Let's break down the steps for both parts of the question.
(a) How many revolutions does each tire make before the car comes to a stop?
1. First, let's find the time it takes for the car to come to a stop. We can use the equation of motion:
v_f = v_i + at
where v_f is the final velocity (zero in this case), v_i is the initial velocity (24.0 m/s), a is the acceleration (-2.10 m/s^2), and t is the time.
Rearranging the equation, we have:
t = (v_f - v_i) / a
Substituting the values, we get:
t = (0 - 24.0) / (-2.10) = 11.43 s (rounded to two decimal places)
2. Now, let's find the distance traveled by each tire. Since the car comes to a stop, the distance traveled by each tire is equal to the circumference of the tire.
Circumference = 2πr, where r is the radius of the tire.
Substituting the values, we get:
Circumference = 2π(0.330) = 2.07 m (rounded to two decimal places)
3. Finally, let's find the number of revolutions. We can calculate the number of revolutions using the formula:
Number of revolutions = distance traveled / circumference
Substituting the values, we have:
Number of revolutions = (24.0 m/s) * (11.43 s) / 2.07 m = 132.17 revolutions (rounded to two decimal places)
Therefore, each tire makes approximately 132.17 revolutions before the car comes to a stop.
(b) What is the angular speed of the wheels when the car has traveled half the total distance?
1. First, let's find the total distance traveled by the car. We can use the equation of motion:
s = ut + (1/2)at^2
where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration.
Since the car comes to a stop, the final distance traveled is half the total distance.
Rearranging the equation, we have:
s = ut + (1/2)at^2
Substituting the values, we get:
(1/2) = (24.0 m/s) * t + (1/2)(-2.10 m/s^2)t^2
Rearranging and solving the quadratic equation, we find:
t ≈ 4.16 s (rounded to two decimal places)
2. Since the car has traveled half the total distance, the distance traveled by each tire is also half of what we calculated in part (a). Therefore, the distance traveled by each tire is approximately 1.035 m (rounded to three decimal places).
3. Now, let's find the angular speed. The angular speed is defined as the change in angle divided by the change in time. Since we know the distance traveled and the radius of the tire, we can calculate the angular speed as follows:
Angular speed = distance traveled / (radius of the tire)
Substituting the values, we have:
Angular speed = 1.035 m / 0.330 m = 3.14 rad/s (rounded to two decimal places)
Therefore, the angular speed of the wheels when the car has traveled half the total distance is approximately 3.14 rad/s.