This can be calculated with the law of conservation of energy. The kinetic energy Ek of the train is completely transformed to potential energy of the spring Ep which stops the train:
Ek=Ep
(1/2)*m*v²=(1/2)*k*x², where m is mass of the train, v is the velocity of the train, k is the force constant of the spring and x is the path the train went while being stopped and also the amount of length the spring compressed.
We solve for k:
(1/2)*m*v²=(1/2)*k*x², 1/2 cancel out:
m*v²=k*x², we divide both sides by x² and get k:
k=(m*v²)/x²={(5*10^5)*(0.5²)}/(0.4²)=781250 N/m
So the force constant of the spring is: k=781250 N/m.
Answer:
<em>I think the answer is C</em>
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Explanation:
Its heavy but not too heavy
From the given information:
- Taking the movement of the Duck in the North as the x-direction
- The movement of the Duck in the East direction as the y-direction
However, we will have to compute the initial velocity and the acceleration of the duck in their vector forms.
<h3>In vector form;</h3>
The initial velocity is:

The acceleration is:

The objective of this question is to determine the speed of the duck at a certain time. Since it is not given, let's assume we are to determine the Duck speed after 4 seconds of accelerating;
Then, it implies that time (t) = 4 seconds.
Using the first equation of motion:

Then, we can replace their values into the equation of motion in order to determine the speed:



Collect like terms:


Thus, the magnitude is:




Therefore, we can conclude that the speed of the duck after 4 seconds is 1.34 m/s
Learn more about vectors here:
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The equation that would allow us to calculate for the acceleration given the distance is written below,
a = (Vf² - Vo²) / 2d
where a is the acceleration, Vf is the final velocity, Vo is the initial velocity, and d is distance.
Substituting the known values,
a = ((84 ft/s)² - (72 ft/s)²) / 2(180 ft) = 5.2 ft/s²
Then, the equation that would relate the initial velocity, distance, acceleration and time is calculated through the equation,
d = Vot + 0.5at²
Substituting the known values,
180 = 72(t) + 0.5(5.2)(t²)
The value of t from the equation is 2.3 s
<em>ANSWER: 2.3 s</em>