The displacement of a particle starting from rest a t = 0 is given byS=6t2–t3. The time in seconds at which the particle will attain zero velocity is (a) 8s (b) 6s (c) 4s (d) 3s
Question
The displacement of a particle starting from rest a t = 0 is given byS=6t2–t3. The time in seconds at which the particle will attain zero velocity is (a) 8s (b) 6s (c) 4s (d) 3s
Solution
To find the time at which the particle will attain zero velocity, we need to find the derivative of the displacement function S(t) = 6t^2 - t^3, which gives us the velocity function.
The derivative of S(t) is S'(t) = 12t - 3t^2.
Setting this equal to zero gives us the times at which the velocity is zero:
12t - 3t^2 = 0 t(12 - 3t) = 0
Setting each factor equal to zero gives us t = 0 and t = 4.
Since the particle starts from rest at t = 0, the time at which the particle will attain zero velocity again is t = 4s.
So, the correct answer is (c) 4s.
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