a car traveling at 30.0m/s undergoes a constant negative accerleration of magnitude of 2.00m/s^2 when the brakes are applied. how many revolutions does each tire make before the car comes to a complete stop,assuming thaat the car does not skid and that the tires have radii of 0.300m?
I agree with Bob
To find the number of revolutions each tire makes before the car comes to a complete stop, we need to follow these steps:
1. Determine the time it takes for the car to come to a complete stop.
2. Calculate the distance traveled by each tire during this time.
3. Convert the distance to revolutions.
Let's break down the steps:
1. Determine the time it takes for the car to come to a complete stop:
When the car comes to a complete stop, its final velocity (vf) is 0 m/s. The initial velocity (vi) is given as 30.0 m/s. The acceleration (a) is -2.00 m/s^2 (negative because it is in the opposite direction of motion). We can use the following equation to find the time (t) it takes for the car to stop:
vf = vi + at
Substituting the given values:
0 = 30.0 + (-2.00) * t
Solving for t:
2.00t = 30.0
t = 30.0 / 2.00
t = 15.0 s
So it takes 15.0 seconds for the car to come to a complete stop.
2. Calculate the distance traveled by each tire during this time:
To find the distance traveled (d), we can use the following equation:
d = vit + 0.5 * a * t^2
Substituting the given values:
d = 30.0 * 15.0 + 0.5 * (-2.00) * (15.0)^2
Simplifying the equation:
d = 450 - 225
d = 225 m
Therefore, each tire travels a distance of 225 meters before the car comes to a complete stop.
3. Convert the distance to revolutions:
Each tire has a radius (r) of 0.300 m. The circumference of a circle is given by C = 2πr. Therefore, the distance traveled by each tire can be converted to the number of revolutions (n) using the formula:
n = d / C
Substituting the values:
n = 225 / (2π * 0.300)
Calculating the value:
n = 225 / (2 * 3.14159 * 0.300)
n ≈ 119.4 revolutions
Therefore, each tire makes approximately 119.4 revolutions before the car comes to a complete stop.
119.37
First find out how far it travels while decelerating. Call that distance X. The divide X by 2 pi R to get the number of tire rotations.
The average speed while decelerating is 15.0 m/s. The time required to decelerate to zero speed is (30.0 m/s)/2 m/s^2 = 15 s
X = (average speed) * t = 225 m
Finally, divide that by 2 pi R.