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The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?
  • a)
    2
  • b)
    5
  • c)
    1
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The trajectory of an object is defined as x = (t - 4)2, what is the ve...
The function for velocity can be derived by differentiating the equation with respect to t. v = 2(t - 4) is the required function. When t = 5, v = 2(5 - 4) = 2.
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Most Upvoted Answer
The trajectory of an object is defined as x = (t - 4)2, what is the ve...
Given Data:
The trajectory of the object is defined as x = (t - 4)^2.

Velocity Calculation:
To calculate the velocity of the object at t = 5, we need to find the derivative of the trajectory function with respect to time (t).
Taking the derivative of x = (t - 4)^2 with respect to t, we get:
dx/dt = 2(t - 4) * (d/dt)(t - 4)
dx/dt = 2(t - 4)
Now, substitute t = 5 into the derivative to find the velocity at t = 5:
dx/dt = 2(5 - 4)
dx/dt = 2
Therefore, the velocity of the object at t = 5 is 2.

Conclusion:
The velocity of the object at t = 5 is 2. Hence, the correct answer is option 'A'.
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Directions:Read the passages and choose the best answer to each question.PassageStudents debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.ObservationsObservation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.Some asteroids also contain carbon and other elements.Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.Hypothesis 1All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.Q.Which of the following assumptions regarding the asteroid belt’s origins is implicit in Hypothesis 1?

Directions:Read the passages and choose the best answer to each question.PassageStudents debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.ObservationsObservation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.Some asteroids also contain carbon and other elements.Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.Hypothesis 1All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.Q. Supporters of Hypothesis 1 would most likely agree that, at the time the asteroid belt formed the planets were

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Directions:Read the passages and choose the best answer to each question.PassageStudents debate 4 hypotheses regarding the origin of the asteroid belt located between Mars and Jupiter, based on the following observations.ObservationsObservation 1- If all of the asteroids were gathered together into one object, the diameter of the object formed would be less than half the diameter of Earth’s Moon.Observation 2- The total mass of the asteroid belt is only 4% that of the Moon. One asteroid alone, Ceres, contains 1/3 of the total mass of the asteroid belt.Observation 3- Asteroids are largely composed of silicate, with some deposits of iron and nickel, a composition proportionately similar to that of the terrestrial planets.Some asteroids also contain carbon and other elements.Observation 4- There is a strong orbital resonance (overlapping gravity) with Jupiter in the region of the asteroid belt, which keeps the asteroids in an orbit around the sun.Observation 5- In reality, asteroids within the belt are very far apart, not clustered together.Observation 6- Within the early solar system, the velocity of collisions within the region of the asteroid belt was much higher than it is currently.Hypothesis 1All of the material that makes up the asteroids in the asteroid belt is similar to that of the material that makes up the terrestrial planets. The velocity of collisions in the early solar system was at one time high enough to break apart planets as they formed. Since one asteroid, Ceres, has 1/3 the total mass of the belt, the asteroids are most likely the result of a partially formed planet that broke apart and became trapped in an orbit between Mars and Jupiter.Hypothesis 2 The material that composes the asteroids is similar to that of the terrestrial planets. The belt likely formed during the same time that the planets were forming, and due to the strong orbital resonance with the gas giant Jupiter and high velocity collisions, chunks of the material were pulled away from various planets and trapped within orbit. This also explains the varying composition of the asteroids throughout the belt.Hypothesis 3 The asteroids could not once have been a planet, because there is not enough material within the entire belt to form a planet-sized object. The lack of material, shown by the total diameter and mass of the objects within the belt, is proof that the asteroids are no more than large particles left over from the formation of the terrestrial planets from a single cloud of material.Hypothesis 4 The asteroids most likely came from somewhere outside the solar system. As they passed through space at varying intervals, they were trapped by the large orbital resonance of Jupiter and formed a “belt.” The vast distances between most of the asteroids in the belt are evidence that they did not come from a singular source, but arrived at different points in the belt’s development.Q. Hypothesis 3 includes the assertion that the asteroids are made up of particles left over from a single cloud of material. This assertion explains which of the following observations?

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The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?a)2b)5c)1d)4Correct answer is option 'A'. Can you explain this answer?
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The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?a)2b)5c)1d)4Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?a)2b)5c)1d)4Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The trajectory of an object is defined as x = (t - 4)2, what is the velocity at t = 5?a)2b)5c)1d)4Correct answer is option 'A'. Can you explain this answer?.
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