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A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be?
Most Upvoted Answer
A particle is moving so that it's displacement is given as s =t3-6t2+3...
Explanation:
To find the velocity of the particle when its acceleration is zero, we need to differentiate the displacement equation twice with respect to time to obtain the acceleration equation. Once we get the acceleration equation, we can set it equal to zero and solve for the time at which it occurs. Then we can substitute this time into the velocity equation to obtain the velocity at that instant.
Derivation:
Step 1: Differentiate the displacement equation to obtain the velocity equation:
s = t3-6t2+3t+4
v = ds/dt = 3t2-12t+3
Step 2: Differentiate the velocity equation to obtain the acceleration equation:
a = dv/dt = 6t-12
Step 3: Set the acceleration equation equal to zero and solve for the time at which it occurs:
a = 6t-12 = 0
t = 2 seconds
Step 4: Substitute the time into the velocity equation to obtain the velocity at that instant:
v = 3t2-12t+3
v = 3(2)2-12(2)+3
v = -15 m/s
Conclusion:
The velocity of the particle at the instant when its acceleration is zero is -15 m/s.
To find the velocity of the particle when its acceleration is zero, we need to differentiate the displacement equation twice with respect to time to obtain the acceleration equation. Once we get the acceleration equation, we can set it equal to zero and solve for the time at which it occurs. Then we can substitute this time into the velocity equation to obtain the velocity at that instant.
Derivation:
Step 1: Differentiate the displacement equation to obtain the velocity equation:
s = t3-6t2+3t+4
v = ds/dt = 3t2-12t+3
Step 2: Differentiate the velocity equation to obtain the acceleration equation:
a = dv/dt = 6t-12
Step 3: Set the acceleration equation equal to zero and solve for the time at which it occurs:
a = 6t-12 = 0
t = 2 seconds
Step 4: Substitute the time into the velocity equation to obtain the velocity at that instant:
v = 3t2-12t+3
v = 3(2)2-12(2)+3
v = -15 m/s
Conclusion:
The velocity of the particle at the instant when its acceleration is zero is -15 m/s.
Community Answer
A particle is moving so that it's displacement is given as s =t3-6t2+3...
Differentiate it two times and put it equal to zero ds/dt=3t^2-12t+3 d^2s/dt^2 = 6t-12 6t-12=0 t=2 sec answer= 2sec
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A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be?.
A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving so that it's displacement is given as s =t3-6t2+3t+4 meter. It's velocity at that instant when it's acceleration is zero will be?.
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