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The displacement of a particle starting from rest (at t=0) is given by s=6t^2-t Find The time in second at which the particle will attain 0 velocity.?
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The displacement of a particle starting from rest (at t=0) is given by...
Problem: Find the time in seconds at which the particle will attain 0 velocity given that the displacement of a particle starting from rest (at t=0) is given by s=6t^2-t.

Solution:

Step 1: Calculate the velocity of the particle

We know that velocity is the derivative of displacement with respect to time. Therefore, the velocity of the particle is given by:

v = ds/dt = 12t - 1

Step 2: Set the velocity equation to 0

To find the time at which the particle will attain 0 velocity, we need to set the velocity equation equal to 0 and solve for t:

12t - 1 = 0

12t = 1

t = 1/12

Therefore, the particle will attain 0 velocity at t = 1/12 seconds.

Step 3: Verify the answer

To verify our answer, we can find the velocity of the particle at t = 1/12 seconds using the velocity equation:

v = 12t - 1

v = (12/12) - 1

v = 0

Since the velocity of the particle at t = 1/12 seconds is 0, our answer is correct.

Conclusion: The particle will attain 0 velocity at t = 1/12 seconds.
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The displacement of a particle starting from rest (at t=0) is given by...
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