The stoplights on a street are designed to keep traffic moving at 24 mi/h. The average length of a street block between traffic
1 answer:
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Answer:
Velocity = 0.4762 m/s
Explanation:
Given the details for the simple harmonic motion from the question as:
Angular frequency, ω = 12 rad/s
Amplitude, A = 0.060 m
Displacement, y = 0.045 m
The initial Energy = U = (1/2) kA²
where A is the amplitude and k is the spring constant.
The final energy is potential and kinetic energy
K + U = (1/2) mv² + (1/2) kx²
where x is the displacement
m is the mass of the object
v is the speed of the object
Since energy is conservative. So, the final and initial energies are equal as:
(1/2) k A² = (1/2) m v² + (1/2) kx²
Using, ω² = k/m, we get:
Velocity:
<u>Velocity = 0.4762 m/s</u>
1) Acceleration of the car in front: -7.89 m/s^2
The only data we need for this part of the problem is:
--> initial velocity of the car
--> coefficient of friction between the car wheels and the road
From the coefficient of friction, we can find the deceleration of the car. In fact, the force of friction is given by
where m is the car's mass and is the acceleration due to gravity. We can find the car's acceleration by using Newton's second law:
And the negative sign means it is a deceleration.
2) Braking distance for the car in front: 48.6 m
This can be found by using the following SUVAT equation:
where
v=0 is the final velocity of the car
u=27.7 m/s is the initial velocity of the car
a=-7.89 m/s^2 is the acceleration of the car
S is the braking distance
By re-arranging the formula, we find S:
3) Minimum safe distance at which you can follow the car: 15.0 m
In this case, we must calculate the thinking distance, which is the distance you travel before hitting the brakes. During this time, the speed of your car is constant, so the thinking distance is given by
After hitting the brakes, your car decelerates at the same rate of the car in front of you, so the braking distance is the same of the other car:
So the total distance your car covers is
At the same time, the car in front of you just covered a distance of 48.6 m. So, in order to avoid the collision, you should travel at a distance equal to