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ACT Exam  >  ACT Questions  >  A body is moving with a constant acceleration... Start Learning for Free
A body is moving with a constant acceleration of 4î + 3ĵ, starting from the origin. What will be the position of the body after 5s?
  • a)
    50î + 37.5ĵ
  • b)
    37.5î + 50ĵ
  • c)
    37.5î – 50ĵ
  • d)
    50î – 37.5ĵ
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A body is moving with a constant acceleration of 4î + 3, startin...
The body’s displacement is given by s = (1/2)at2. The body starts from the origin hence, the total displacement is the final position of the body. Therefore, after putting in the values, we get, s = (1/2)(4î + 3ĵ)*52 = 50î + 37.5ĵ.
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Most Upvoted Answer
A body is moving with a constant acceleration of 4î + 3, startin...
Understanding the Problem
The body is moving with a constant acceleration, given as 4i + 3j. We need to find its position after 5 seconds, starting from the origin.
Given Variables
- Initial position (s0) = 0 (origin)
- Initial velocity (u) = 0 (since it starts from rest)
- Acceleration (a) = 4i + 3j
- Time (t) = 5 seconds
Using the Equation of Motion
The position vector (s) after time t under constant acceleration can be calculated using the formula:
s = s0 + ut + (1/2)at²
Since the initial position and velocity are both zero, the equation simplifies to:
s = (1/2)at²
Calculating the Position
- Substitute the acceleration and time into the formula:
s = (1/2)(4i + 3j)(5)²
- Calculate (5)²:
(5)² = 25
- Now, plug this value into the equation:
s = (1/2)(4i + 3j)(25)
s = (1/2)(100i + 75j)
- Simplifying further:
s = 50i + 37.5j
Final Result
After 5 seconds, the position of the body will be:
s = 50i + 37.5j
Thus, the correct answer is option A: 50i + 37.5j.
This detailed calculation confirms that option A is indeed the correct choice.
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A body is moving with a constant acceleration of 4î + 3, starting from the origin. What will be the position of the body after 5s?a)50î + 37.5b)37.5î + 50c)37.5î – 50d)50î – 37.5Correct answer is option 'A'. Can you explain this answer?
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