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A body has an initial velocity of 3 m/s and has anacceleration of 1 ms-2 normal to the direction of the initial velocity. Then its velocity 4 s after the start is
- a)7 ms-1 along the direction of initial velocity
- b)7 ms-1 along the normal to the direction of initialvelocity.
- c)7 ms-1 midway between the two directions
- d)5 ms-1 at an angle tan-1 (4/3) with the direction ofinitial velocity.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A body has an initial velocity of 3 m/s and has anacceleration of 1 ms...
Explanation:
To solve the problem, we need to use the equations of motion.
Equations of Motion:
- v = u + at (final velocity = initial velocity + acceleration x time)
- s = ut + 1/2 at^2 (distance = initial velocity x time + 1/2 x acceleration x time^2)
- v^2 = u^2 + 2as (final velocity^2 = initial velocity^2 + 2 x acceleration x distance)
Given:
- Initial velocity (u) = 3 m/s
- Acceleration (a) = 1 m/s^2 (normal to the direction of initial velocity)
- Time (t) = 4 s
Solution:
1. Calculate the distance travelled by the body in 4 seconds:
- s = ut + 1/2 at^2
- s = 3 x 4 + 1/2 x 1 x 4^2
- s = 12 + 8
- s = 20 m
2. Calculate the final velocity of the body:
- v^2 = u^2 + 2as
- v^2 = 3^2 + 2 x 1 x 20
- v^2 = 9 + 40
- v^2 = 49
- v = √49
- v = 7 m/s
3. Determine the direction of the final velocity using trigonometry:
- tanθ = perpendicular/base
- tanθ = 4/3
- θ = tan^-1(4/3)
- θ ≈ 53.13°
4. Therefore, the final velocity of the body is 7 m/s at an angle of 53.13° with the direction of the initial velocity. The correct answer is option D.
To solve the problem, we need to use the equations of motion.
Equations of Motion:
- v = u + at (final velocity = initial velocity + acceleration x time)
- s = ut + 1/2 at^2 (distance = initial velocity x time + 1/2 x acceleration x time^2)
- v^2 = u^2 + 2as (final velocity^2 = initial velocity^2 + 2 x acceleration x distance)
Given:
- Initial velocity (u) = 3 m/s
- Acceleration (a) = 1 m/s^2 (normal to the direction of initial velocity)
- Time (t) = 4 s
Solution:
1. Calculate the distance travelled by the body in 4 seconds:
- s = ut + 1/2 at^2
- s = 3 x 4 + 1/2 x 1 x 4^2
- s = 12 + 8
- s = 20 m
2. Calculate the final velocity of the body:
- v^2 = u^2 + 2as
- v^2 = 3^2 + 2 x 1 x 20
- v^2 = 9 + 40
- v^2 = 49
- v = √49
- v = 7 m/s
3. Determine the direction of the final velocity using trigonometry:
- tanθ = perpendicular/base
- tanθ = 4/3
- θ = tan^-1(4/3)
- θ ≈ 53.13°
4. Therefore, the final velocity of the body is 7 m/s at an angle of 53.13° with the direction of the initial velocity. The correct answer is option D.
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Community Answer
A body has an initial velocity of 3 m/s and has anacceleration of 1 ms...
After 4 sec i.e Vx = 3 m/s in vertical motion intial velocity is zero and so final velocity in vertical motion Vv = uy+at Vy = 0+1*4 = 4 m/s since acceleration is normal to the initial velocity so net velocity after 4 sec = v' = (4^2+3^2)^1/2 = 5 m/s direction theta = 5 m/s tan inverse (vy/vx) = tan inverse (4/3)
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A body has an initial velocity of 3 m/s and has anacceleration of 1 ms-2 normal to the direction of the initial velocity. Then its velocity 4 s after the start isa)7 ms-1 along the direction of initial velocityb)7 ms-1 along the normal to the direction of initialvelocity.c)7 ms-1 midway between the two directionsd)5 ms-1 at an angle tan-1 (4/3) with the direction ofinitial velocity.Correct answer is option 'D'. Can you explain this answer?
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A body has an initial velocity of 3 m/s and has anacceleration of 1 ms-2 normal to the direction of the initial velocity. Then its velocity 4 s after the start isa)7 ms-1 along the direction of initial velocityb)7 ms-1 along the normal to the direction of initialvelocity.c)7 ms-1 midway between the two directionsd)5 ms-1 at an angle tan-1 (4/3) with the direction ofinitial velocity.Correct answer is option 'D'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A body has an initial velocity of 3 m/s and has anacceleration of 1 ms-2 normal to the direction of the initial velocity. Then its velocity 4 s after the start isa)7 ms-1 along the direction of initial velocityb)7 ms-1 along the normal to the direction of initialvelocity.c)7 ms-1 midway between the two directionsd)5 ms-1 at an angle tan-1 (4/3) with the direction ofinitial velocity.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body has an initial velocity of 3 m/s and has anacceleration of 1 ms-2 normal to the direction of the initial velocity. Then its velocity 4 s after the start isa)7 ms-1 along the direction of initial velocityb)7 ms-1 along the normal to the direction of initialvelocity.c)7 ms-1 midway between the two directionsd)5 ms-1 at an angle tan-1 (4/3) with the direction ofinitial velocity.Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice A body has an initial velocity of 3 m/s and has anacceleration of 1 ms-2 normal to the direction of the initial velocity. Then its velocity 4 s after the start isa)7 ms-1 along the direction of initial velocityb)7 ms-1 along the normal to the direction of initialvelocity.c)7 ms-1 midway between the two directionsd)5 ms-1 at an angle tan-1 (4/3) with the direction ofinitial velocity.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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