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A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.
Correct answer is '1125'. Can you explain this answer?
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A particle of mass 2 kg is moving along the x-axis. There is no force ...
Force acting on particle
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A particle of mass 2 kg is moving along the x-axis. There is no force ...
Given:
- Mass of the particle (m) = 2 kg
- Force acting on the particle (F(t)) = 6t^2 N/s^2
- Initial velocity of the particle at t = 0 (v0) = 1000 m/s
- Time interval between t = 0 sec and t = 5 sec when force is acting on the particle
To find:
Velocity of the particle at t = 10 sec (v)
Approach:
To find the velocity of the particle at t = 10 sec, we need to calculate the total change in momentum of the particle over the time interval between t = 0 sec and t = 10 sec. Since there is no force acting on the particle after t = 5 sec, the momentum of the particle remains constant from t = 5 sec to t = 10 sec.
Step 1: Calculate the change in momentum from t = 0 sec to t = 5 sec
- The force acting on the particle is given by F(t) = 6t^2 N/s^2.
- The acceleration of the particle (a) can be calculated using Newton's second law, F = ma.
- Integrating the acceleration with respect to time will give the change in velocity (Δv).
- Integrating the change in velocity with respect to time will give the change in momentum (Δp).
Step 2: Calculate the change in momentum from t = 5 sec to t = 10 sec
- Since there is no force acting on the particle after t = 5 sec, the momentum remains constant. Therefore, the change in momentum is zero.
Step 3: Calculate the final velocity at t = 10 sec
- The final momentum at t = 10 sec is the sum of the initial momentum and the change in momentum from t = 0 sec to t = 5 sec.
- The final velocity can be calculated by dividing the final momentum by the mass of the particle.
Calculation:
Step 1:
- The acceleration of the particle is given by a = F(t)/m = (6t^2)/2 = 3t^2 m/s^2.
- Integrating the acceleration, we get the change in velocity as Δv = ∫(3t^2)dt = t^3 m/s.
- Integrating the change in velocity, we get the change in momentum as Δp = ∫(t^3)dt = (1/4)t^4 kg.m/s.
Step 2:
- There is no force acting on the particle after t = 5 sec, so the change in momentum is zero, i.e., Δp = 0 kg.m/s.
Step 3:
- The final momentum at t = 10 sec is the sum of the initial momentum and the change in momentum from t = 0 sec to t = 5 sec, i.e., p = m*v0 + Δp.
- The final velocity at t = 10 sec is given by v = p/m.
Substituting the values:
- Δp = (1/4)*(5^4) = 625/4 kg.m/s
- p
- Mass of the particle (m) = 2 kg
- Force acting on the particle (F(t)) = 6t^2 N/s^2
- Initial velocity of the particle at t = 0 (v0) = 1000 m/s
- Time interval between t = 0 sec and t = 5 sec when force is acting on the particle
To find:
Velocity of the particle at t = 10 sec (v)
Approach:
To find the velocity of the particle at t = 10 sec, we need to calculate the total change in momentum of the particle over the time interval between t = 0 sec and t = 10 sec. Since there is no force acting on the particle after t = 5 sec, the momentum of the particle remains constant from t = 5 sec to t = 10 sec.
Step 1: Calculate the change in momentum from t = 0 sec to t = 5 sec
- The force acting on the particle is given by F(t) = 6t^2 N/s^2.
- The acceleration of the particle (a) can be calculated using Newton's second law, F = ma.
- Integrating the acceleration with respect to time will give the change in velocity (Δv).
- Integrating the change in velocity with respect to time will give the change in momentum (Δp).
Step 2: Calculate the change in momentum from t = 5 sec to t = 10 sec
- Since there is no force acting on the particle after t = 5 sec, the momentum remains constant. Therefore, the change in momentum is zero.
Step 3: Calculate the final velocity at t = 10 sec
- The final momentum at t = 10 sec is the sum of the initial momentum and the change in momentum from t = 0 sec to t = 5 sec.
- The final velocity can be calculated by dividing the final momentum by the mass of the particle.
Calculation:
Step 1:
- The acceleration of the particle is given by a = F(t)/m = (6t^2)/2 = 3t^2 m/s^2.
- Integrating the acceleration, we get the change in velocity as Δv = ∫(3t^2)dt = t^3 m/s.
- Integrating the change in velocity, we get the change in momentum as Δp = ∫(t^3)dt = (1/4)t^4 kg.m/s.
Step 2:
- There is no force acting on the particle after t = 5 sec, so the change in momentum is zero, i.e., Δp = 0 kg.m/s.
Step 3:
- The final momentum at t = 10 sec is the sum of the initial momentum and the change in momentum from t = 0 sec to t = 5 sec, i.e., p = m*v0 + Δp.
- The final velocity at t = 10 sec is given by v = p/m.
Substituting the values:
- Δp = (1/4)*(5^4) = 625/4 kg.m/s
- p
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A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer?
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A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer?.
A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 2 kg is moving along the x-axis. There is no force on the particle except during the time interval between t = Osec and t = 5 sec, when a force of the form F(t) = 6t2N/S2 acts on it. If the velocity o f the particle at t = 0 is 1000m/sec then calculate its velocity at t=10 sec.Correct answer is '1125'. Can you explain this answer?.
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