Answer:
b) 6
Explanation:
Given
v(t)=3t²+6t
X(0) = 2
X(1) = ?
Knowing that
v(t)=3t²+6t = dX/dt
⇒ ∫dX = ∫(3t²+6t)dt
⇒ X - X₀ = t³ + 3t²
⇒ X(t) = X₀ + t³ + 3t²
If X(0) = 2
⇒ X(0) = X₀ + (0)³ + 3(0)² = 2
⇒ X₀ = 2
then we have
X(t) = t³ + 3t² + 2
when
t = 1
X(1) = (1)³ + 3(1)² + 2
X(1) = 6
Answer:
298,220 N
Explanation:
Let the force on car three is T_23-T_34
Since net force= ma
from newton's second law we have
T_23-T_34 = ma
therefore,
T_23-T_34 = 37000×0.62
T_23= 22940+T_34
now, we need to calculate
T_34
Notice that T_34 is accelerating all 12 cars behind 3rd car by at a rate of 0.62 m/s^2
F= ma
So, F= 12×37000×0.62= 22940×12= 275280 N
T_23 =22940+T_34= 22940+ 275280= 298,220 N
therefore, the tension in the coupling between the second and third cars
= 298,220 N
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Answer:
Explanation:
Since the equation for the illumination of an object, i.e. the brightness of the light, is <em>inversely proportional to the square of the distance from the light source</em>, the form of the function is:
Where x is the distance between the object and the light force, k is the constant of proportionality, and f(x) is the brightness.
Then, if you move halfway to the lamp the new distance is x/2 and the new brightness (call if F) is :

Then, you have found that the light is 4 times as bright as it originally was.
Answer:
D. Hydrogen combines with oxygen to form water.
Explanation:
Hydrogen combining with oxygen to form water is a typical example of chemical reaction.
During a chemical reaction, atoms of elements are rearranged. Most chemical reactions obey the law of conservation of mass which states that "matter is neither created nor destroyed in a chemical reaction but atoms are simply rearranged".
The other choices given are nuclear reactions. In such reactions, atoms are not rearranged but are simply destroyed and made in the process.