Question

The velocity of the particle at any time t is given by $v = 2t(3 - t)ms^{- 1}$

At what time is its velocity maximum?

• A. 2 s
• B. 3 s
• C. $\frac{2}{3}s$
• D. $\frac{3}{2}s$

Answer 1

Answer: (D)

$\frac{3}{2}s$

Answer 2

Given $v = 2t(3 - t)orv = 6t - 2t^{2}$

$\frac{dv}{dt} = 6 - 4t$

At maximum velocity, $\frac{dy}{dt} = 0$

$\therefore 6 - 4t = 0ort = \frac{3}{2}s$