Question

The driver of a car traveling at 36.4 m/s applies the brakes and undergoes a constant

deceleration of 0.94 m/s2

How many revolutions does each tire make
before the car comes to a stop, assuming that
the car does not skid and that the tires have
radii of 0.35 m?
Answer in units of rev

Answer 1

The car's tires make 580.9 revolutions before the car comes to a stop.

Step-by-step explanation:

To find the number of revolutions the tires make before the car comes to a stop, we need to calculate the time it takes for the car to stop first. We can use the equation:

vf = vi + at

Where vf is the final velocity (0 m/s), vi is the initial velocity (36.4 m/s), a is the acceleration (-0.94 m/s^2), and t is the time it takes for the car to stop. Rearranging the equation, we get:

t = (vf - vi) / a

Substituting the given values, we get:

t = (0 - 36.4) / -0.94 = 38.72 s

Next, we can calculate the angular acceleration using the formula:

α = a / r

Where α is the angular acceleration, a is the linear acceleration, and r is the radius of the tire. Substituting the given values, we get:

α = -0.94 / 0.35 = -2.69 rad/s^2

Finally, we can calculate the number of revolutions using the formula:

number of revolutions = (initial angular velocity * time) / (2π)

Substituting the given values, we get:

number of revolutions = (95.0 * 38.72) / (2π) = 580.9 rev

Answer 2

Each tire make before the car comes to a stop is 322 revolutions.

Step-by-step explanation:

Given that,

Initial speed of the car, u = 36.4 m/s

Finally, it stops, v = 0

Deceleration of the car,
`a=-0.94\ m/s^2`

Radius of the tire, r = 0.35 m

Let d is the displacement of the car. It can be calculated using third equation of kinematics as :

`d=(v^2-u^2)/(2a)`

`d=(-(36.4)^2)/(2* -0.94)`

d = 704.76 meters

The distance covered in 1 revolution,

`x=2\pi r`

`x=2\pi * 0.35`

x = 2.19 m

Let n are the number of revolution, so,

`n=(704.76)/(2.19)`

n = 321.8

or

n = 322 revolutions

So, each tire make before the car comes to a stop is 322 revolutions. Hence, this is the required solution.