A car initially traveling at 26 m/s hits the brakes, generating a constant acceleration of -2 m/s2. Under this acceleration, the car comes to a rest. If the tires have radii of 0.33 m, how many revolutions does each tire make as the car slows down and stops? Assume no skidding.
s=v²/2•a =26²/2•2=…
N=s/2•π•R=..
To find the number of revolutions each tire makes as the car slows down and stops, we need to determine the distance traveled by each tire.
First, we need to find the time it takes for the car to come to a stop. We can use the 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.
Given:
Initial velocity (u) = 26 m/s
Acceleration (a) = -2 m/s^2 (negative because it is deceleration)
Final velocity (v) = 0 m/s (since the car comes to rest)
Plugging these values into the equation, we get:
0^2 = 26^2 + 2(-2)s
Simplifying, we have:
676 = 4s
s = 169 m
Now, let's find the circumference of each tire using the radius:
Circumference = 2πr
Circumference = 2π(0.33 m)
Circumference ≈ 2.07 m
Finally, we can calculate the number of revolutions each tire makes by dividing the distance traveled (s) by the circumference of each tire:
Number of revolutions = s / Circumference
Number of revolutions = 169 m / 2.07 m
Number of revolutions ≈ 81.64 revolutions
Therefore, each tire makes approximately 81.64 revolutions as the car slows down and stops.