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In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is?
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In the figure shown, A and B are two particles which start from rest. ...
Problem:
In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is?

Solution:

Given:
- Acceleration of particle A, a = 3 m/s²
- Acceleration of particle B towards A, b = 4 m/s²
- Time taken by particle B to meet A, t = 2lb b² a

Approach:
- Use the equations of motion to find the distance travelled by A and B in time t
- Equate the distances travelled by A and B to find the point of intersection
- Use the distance travelled by A to find the value of acceleration a

Equations of Motion:
- Distance travelled by a particle with acceleration a in time t, S = 1/2 a t²
- Final velocity of a particle with acceleration a in time t, v = a t

Distance Travelled by A:
- Distance travelled by A in time t, SA = 1/2 a t² = 1/2 * 3 * (2lb b² a)² = 3lb² a³

Distance Travelled by B:
- Velocity of B after time t, vb = b t = 4 (2lb b² a) = 8lb b³ a
- Distance travelled by B in time t, SB = vb t = 8lb² b³ a²

Point of Intersection:
- SA = SB
- 3lb² a³ = 8lb² b³ a²
- a = 24 b³ / (8 b² + 3 a²)

Final Answer:
- Substituting the value of b = 4 m/s², we get a = 6 m/s²

Therefore, the acceleration of particle A is 6 m/s².
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In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is?
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In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is?.
Solutions for In the figure shown, A and B are two particles which start from rest. A has constant acceleration a = 3 m/s² in the direction shown. B also increases its speed at a constant rate b = 4m/s², but the direction of velocity is always towards A. If the time after which B meets A is 2lb b² a then, a (in Sl unit) is? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
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