a car is traveling with a speed of 15 m/s on a stratight horzontal highway. the wheels of the car have a radius of 50cm.if the car then speeds up with an acceleration of 2 m/s for 5s, find the number of revolution of the wheels during this period.
C=2pi*r=6.28*50=314cm/rev = 3.14m/rev.
a = 2 / 5 = 0.4m/s^2.
d = Vo*t + 0.5at^2,
d = 15*5 + 0.5*0.4*5^2,
d = 75 + 5 = 80m.
Rev = 80m / 3.14m/rev = 25.5.
To find the number of revolutions of the wheels during this period, we need to calculate the angular displacement of the wheels.
First, let's convert the radius of the wheels to meters:
50 cm = 0.5 meters
Now let's find the initial angular velocity of the wheels.
The linear velocity of a point on the edge of a rotating object is given by the product of its angular velocity and the radius.
So, for the initial velocity of the car (15 m/s), we can write the equation:
15 m/s = ω * 0.5 m
where ω is the initial angular velocity of the wheels in radians per second.
Solving for ω, we get:
ω = 15 m/s / 0.5 m
ω = 30 radians/s
Next, let's calculate the final angular velocity of the wheels after accelerating for 5 seconds.
The final angular velocity can be calculated using the equation:
ωf = ωi + α * t
where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration (which is equal to the linear acceleration divided by the radius), and t is the time.
The angular acceleration can be calculated as:
α = a / r
where a is the linear acceleration and r is the radius.
Using the given values, we can substitute them into the equation:
α = 2 m/s² / 0.5 m
α = 4 radians/s²
Now we can calculate the final angular velocity:
ωf = 30 radians/s + (4 radians/s² * 5 s)
ωf = 50 radians/s
Finally, we can calculate the angular displacement using the equation:
θ = ωi * t + (1/2) * α * t²
where θ is the angular displacement.
Substituting the given values:
θ = 30 radians/s * 5 s + (1/2) * 4 radians/s² * (5 s)²
θ = 150 radians + 50 radians
θ = 200 radians
To find the number of revolutions, we need to convert this angular displacement to revolutions.
One revolution is equal to 2π radians. So, the number of revolutions can be calculated as:
Number of revolutions = angular displacement / (2π radians)
Substituting the values:
Number of revolutions = 200 radians / (2π radians)
Number of revolutions ≈ 31.832
Therefore, during this period, the wheels of the car make approximately 31.832 revolutions.