Question

The driver of a car traveling at 26.1 m/s applies the brakes and undergoes a constant deceleration of 1.64 m/s 2 . 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 0.18 m? Answer in units of rev.

Answer 1

To calculate the number of revolutions a tire makes before the car comes to a stop, we first find the total distance traveled during deceleration, then divide that by the tire's circumference. Kinematic equations and the relation between linear and angular motions are used in the process.

Step-by-step explanation:

The subject of this question is Physics, and it's likely intended for high school students studying dynamics and circular motion. To solve the problem, we use kinematics and the relationship between linear and angular quantities.

Step-by-step Solution

1. First, we must find the total distance the car travels before it comes to a stop using the kinematic equation: s = (v^2 - u^2) / (2 * a), where s is the displacement, v is the final velocity (0 m/s, since the car stops), u is the initial velocity (26.1 m/s), and a is the deceleration (-1.64 m/s^2).
2. Next, we find the total number of revolutions by dividing the total distance by the circumference of the tire using the formula: revolutions = distance / (2 * π * radius).
3. After performing the calculations, we determine the total number of revolutions the tires make before the car comes to a stop.

Answer 2

184 revolutions

Step-by-step explanation:

We will calculate the distance covered for by the car after the brakes are applied. We will apply the following equation of motion:

V^2=U^2 +2as where V is the final velocity, U is the initial velocity, a is the acceleration and s is the distance covered during that acceleration.

0=26.1^2 -2*1.64*s (-ve because it is decelerating).

S=207.7 or 208;

Circumference of the tire = 2
`\pi`r where r is the radius.

Circumference = 1.13

Distance / circumference = # of revolutions.