A car is traveling 30 m/s undergoes a constant negative acceleration of magnitude to meters per second squared when the brakes are applied how many revolutions does each tire make before the car comes to stop assuming that the car does not get on the tires have radius of 30 cm
try again, this time providing the missing numbers, and constructing sentences that make sense.
v = Vi + a t
here Vi = 30 and a = -2 m/s^2 (I guess)
so v = 30 - 2 t
so when v = 0, stopped
t = 15 seconds
how far did it go?
x = Vi t + (1/2)at^2 = 30 (15) - 1 * 225 = 225 meters
or another way average speed during meltdown = 15 m/s for 15 seconds
so 15*15 = 225 again
tire circumference = 2 pi R = 2 pi * 0.30
revolutions = 225 / circumferrence
To determine the number of revolutions each tire makes before the car comes to a stop, we need to find out the time it takes for the car to stop and then calculate the number of revolutions based on the linear motion of the car.
First, let's find the time it takes for the car to stop. We can use the formula:
v = u + at
Where:
v = final velocity (0 m/s, as the car comes to a stop)
u = initial velocity (30 m/s)
a = acceleration (-t)
Rearranging the formula to solve for time (t):
t = (v - u) / a
Substituting the given values:
t = (0 - 30) / (-t)
Simplifying further:
t = 30 / t
t^2 = 30
t ≈ √30
t ≈ 5.48 s (rounded to two decimal places)
Now that we know the time it takes for the car to stop, we can calculate the distance traveled before coming to a stop using the formula:
s = ut + (1/2)at^2
Where:
s = distance
u = initial velocity (30 m/s)
t = time (5.48 s)
a = acceleration (-t)
Substituting the given values:
s = 30 * 5.48 + (1/2) * (-t) * (5.48)^2
s ≈ 82.2 - (1/2) * t * 30
s ≈ 82.2 - 75.4
s ≈ 6.8 m
Next, we need to calculate the distance covered by each tire in terms of revolutions. The distance covered by each tire in one revolution is equal to the circumference of the tire.
Since the radius of each tire is given as 30 cm, the circumference can be calculated as:
C = 2πr
Where:
C = circumference
r = radius (30 cm or 0.3 m)
Substituting the value:
C = 2 * π * 0.3
C ≈ 1.89 m
Now, to find the number of revolutions, we divide the total distance covered by one tire by the circumference:
Revolutions = s / C
Substituting the values:
Revolutions ≈ 6.8 / 1.89
Revolutions ≈ 3.60 (rounded to two decimal places)
Therefore, each tire makes approximately 3.60 revolutions before the car comes to a stop.