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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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A and B are two particles which start from rest. A has constant accele...
**Question Analysis:**
We are given the accelerations of two particles, A and B. Particle A has a constant acceleration of 3 m/s² in a certain direction, while particle B has a constant acceleration of 4 m/s² towards particle A. We need to find the value of acceleration a in SI units, given that the time after which particle B meets particle A is 2lb b² a.
**Solution:**
To solve this problem, we can use the equations of motion to find the time it takes for particle B to meet particle A. Let's break down the solution into steps:
**Step 1: Finding the time it takes for particle B to meet particle A:**
We can use the equation of motion for particle A to find its displacement. Since particle A starts from rest, the equation becomes:
s_A = 0.5 * a * t²
where s_A is the displacement of particle A and t is the time taken. We know that the acceleration of particle A is given as a = 3 m/s².
Next, we can use the equation of motion for particle B to find its displacement. Since particle B starts from rest and has a constant acceleration of 4 m/s² towards particle A, the equation becomes:
s_B = 0.5 * b * t²
where s_B is the displacement of particle B and t is the time taken. We know that the acceleration of particle B is given as b = 4 m/s².
Since both particles start from rest, the total displacement of particle A and particle B should be equal when they meet. Therefore, we can equate their displacements:
0.5 * a * t² = 0.5 * b * t²
**Step 2: Solving for time t:**
To solve for time t, we can cancel out the common terms and rearrange the equation:
a * t² = b * t²
Dividing both sides by t², we get:
a = b
Therefore, the acceleration a is equal to the acceleration b.
**Step 3: Finding the value of acceleration a in SI units:**
From step 2, we know that the acceleration a is equal to the acceleration b, which is given as 4 m/s². Therefore, the value of acceleration a in SI units is 4 m/s².
**Answer:**
The value of acceleration a in SI units is 4 m/s².
We are given the accelerations of two particles, A and B. Particle A has a constant acceleration of 3 m/s² in a certain direction, while particle B has a constant acceleration of 4 m/s² towards particle A. We need to find the value of acceleration a in SI units, given that the time after which particle B meets particle A is 2lb b² a.
**Solution:**
To solve this problem, we can use the equations of motion to find the time it takes for particle B to meet particle A. Let's break down the solution into steps:
**Step 1: Finding the time it takes for particle B to meet particle A:**
We can use the equation of motion for particle A to find its displacement. Since particle A starts from rest, the equation becomes:
s_A = 0.5 * a * t²
where s_A is the displacement of particle A and t is the time taken. We know that the acceleration of particle A is given as a = 3 m/s².
Next, we can use the equation of motion for particle B to find its displacement. Since particle B starts from rest and has a constant acceleration of 4 m/s² towards particle A, the equation becomes:
s_B = 0.5 * b * t²
where s_B is the displacement of particle B and t is the time taken. We know that the acceleration of particle B is given as b = 4 m/s².
Since both particles start from rest, the total displacement of particle A and particle B should be equal when they meet. Therefore, we can equate their displacements:
0.5 * a * t² = 0.5 * b * t²
**Step 2: Solving for time t:**
To solve for time t, we can cancel out the common terms and rearrange the equation:
a * t² = b * t²
Dividing both sides by t², we get:
a = b
Therefore, the acceleration a is equal to the acceleration b.
**Step 3: Finding the value of acceleration a in SI units:**
From step 2, we know that the acceleration a is equal to the acceleration b, which is given as 4 m/s². Therefore, the value of acceleration a in SI units is 4 m/s².
**Answer:**
The value of acceleration a in SI units is 4 m/s².
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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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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 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 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?.
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 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 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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