A car with 80cm diameter wheel starts from rest accelerates uniformly to a speed of 15 m/s in 30 second. Through How many revolutions did each wheel turn in this time?
I mean 89.5 revolutions :)
first find the acceleration : a = (V - u)/t = 0.5 m/s2
the next step is finding the velocity : V = a.t = 15m/s
then the distance covered by the car : S = 1/2 . at2 = 225m
then the next step is finding the circumference of the wheel : C = 2x 3.14 x r = 2.51m/rev
then for the distance covered 225m the wheel revolved is : 225/2.51 = 89.6 revolution
dv/dt = acceleration = 15m/s / 30s = 0.50 meters/s
v = at = 0.50 * 30
x = (1/2) a t^2 = 0.25 (30)^2 = 225 meters
circumference = pi d = 3.14* 0.80 =2.51meters /revilution
so
225 / 2.51 = 89.6 meters
To find out how many revolutions each wheel turned, we first need to convert the given diameter of the wheel from centimeters (cm) to meters (m).
Given:
Diameter of the wheel = 80 cm
Since the diameter is twice the radius of the wheel, we can find the radius by dividing the diameter by 2:
Radius of the wheel = Diameter / 2 = 80 cm / 2 = 40 cm
Next, we need to convert the radius from centimeters to meters:
Radius of the wheel = 40 cm * (1 m / 100 cm) = 0.4 m
Now, we need to find the circumference of the wheel, which is the distance traveled by the wheel in one revolution. The circumference can be calculated using the formula:
Circumference = 2 * π * Radius
Circumference of the wheel = 2 * π * 0.4 m
Next, we need to calculate the distance traveled by the car. We know that the car accelerated uniformly from rest to a speed of 15 m/s in 30 seconds.
Using the equation of motion:
v = u + at
where:
v = final velocity = 15 m/s
u = initial velocity (rest) = 0 m/s
a = acceleration
t = time taken = 30 s
We can rearrange the equation to solve for acceleration (a):
a = (v - u) / t
Substituting the values:
a = (15 m/s - 0 m/s) / 30 s
Now that we have the acceleration, we can use the formula for distance traveled during uniformly accelerated motion:
Distance (s) = u * t + (1/2) * a * t^2
Since the car started from rest, the initial velocity (u) is 0 m/s. Substituting the values:
Distance = 0 * 30 s + (1/2) * a * (30 s)^2
Finally, we can calculate the number of revolutions using the formula:
Number of revolutions = Distance traveled / Circumference
Substituting the values, we can now solve for the number of revolutions each wheel turned.