In a physics experiment (NEET context), the displacement of a particle is given by s = 6t² - t³. At what time 't' is the velocity maximum?

Model Answer & Options

Source: Extra Practice

t = 4

t = 2

t = 6

t = 0

Explanation

Velocity v = ds/dt = 12t - 3t². To find the maximum velocity, we differentiate v with respect to t: dv/dt = 12 - 6t. Setting dv/dt = 0 gives 6t = 12, so t = 2. To confirm it's a maximum, d²v/dt² = -6 (negative). Thus, the velocity is maximum at t = 2 units of time.

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