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The displacement of a particle starting from rest (at t = 0) is given by s = 6t2-t3 . The time in seconds at which the particle will attain zero velocity again, is
- a)6
- b)4
- c)2
- d)8
Correct answer is option 'B'. Can you explain this answer?
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The displacement of a particle starting from rest (at t = 0) is given ...
v = ds/dt
v = 12t - 3t2
0 = 3t (4 - t)
⇒ t = 0 or 4
Here t = 0 is not realistic so at t = 4 the velocity will be zero.
Thus, the particle will attain zero velocity at the time of 4 seconds.
⇒ t = 0 or 4
Here t = 0 is not realistic so at t = 4 the velocity will be zero.
Thus, the particle will attain zero velocity at the time of 4 seconds.
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The displacement of a particle starting from rest (at t = 0) is given ...
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The displacement of a particle starting from rest (at t = 0) is given ...
Given: s = 6t² - t³
To find: Time at which particle will attain zero velocity again
Velocity of a particle can be found by differentiating its displacement with respect to time.
v = ds/dt
v = 12t - 3t²
To find the time at which particle will attain zero velocity again, we need to equate the above equation to zero.
12t - 3t² = 0
3t(4 - t) = 0
The above equation will be zero when either 3t = 0 or 4 - t = 0.
When 3t = 0,
t = 0
When 4 - t = 0,
t = 4
Therefore, the particle will attain zero velocity again at time t = 4 seconds.
Hence, the correct option is (b) 4.
To find: Time at which particle will attain zero velocity again
Velocity of a particle can be found by differentiating its displacement with respect to time.
v = ds/dt
v = 12t - 3t²
To find the time at which particle will attain zero velocity again, we need to equate the above equation to zero.
12t - 3t² = 0
3t(4 - t) = 0
The above equation will be zero when either 3t = 0 or 4 - t = 0.
When 3t = 0,
t = 0
When 4 - t = 0,
t = 4
Therefore, the particle will attain zero velocity again at time t = 4 seconds.
Hence, the correct option is (b) 4.
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