A car accelerates uniformly from rest and reaches a speed of 21.4 m/s in 5.1 s. The diameter of a tire is 38.2 cm.
Find the number of revolutions the tire makes during this motion, assuming no slip-ping.
Answer in units of rev.
To find the number of revolutions the tire makes, we need to find the distance the car travels in terms of the circumference of the tire.
First, we convert the diameter of the tire to the radius:
radius = diameter/2 = 38.2 cm/2 = 19.1 cm.
Now, we need to find the distance the car travels in meters. We can use the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2.
Since the car starts from rest, the initial velocity is 0 m/s.
Acceleration can be found using the equation:
acceleration = (final velocity - initial velocity)/time.
acceleration = (21.4 m/s - 0 m/s) / 5.1 s = 4.2 m/s^2.
Plugging the values into the equation, we get:
distance = 0 m/s * 5.1 s + (1/2) * 4.2 m/s^2 * (5.1 s)^2
Calculating the value, we find:
distance = 54.459 m.
Now, we can find the number of revolutions the tire makes by dividing the distance traveled by the circumference of the tire:
number of revolutions = distance / circumference of tire
= 54.459 m / (2 * π * radius)
= 54.459 m / (2 * π * 0.191 m)
= 142.65 rev.
Therefore, the car makes approximately 142.65 revolutions.