The velocity of the particle at any time t is given by v = 2t(3 - t) m s-1. At what time is its velocity maximum ?

Question

The velocity of the particle at any time t is given by v = 2t(3 - t) m s-1. At what time is its velocity maximum ? (A) 2 s (B) 3 s (C) (2/3)s (D) (3/2)s

Tardigrade Admin · Accepted Answer

Given: v = 2t(3 - t) or v = 6t-2t2 (dv/dt)=6-4t ; For maximum velocity, (dv/dt)=0 ∴ 6-4t=0 or t=(3/2)s

Q. The velocity of the particle at any time $t$ is given by $v = 2 t (3 - t) m s^{- 1}$ . At what time is its velocity maximum ?

$2 s$

$3 s$

$\frac{2}{3} s$

$\frac{3}{2} s$

Given : $v = 2 t (3 - t)$ or $v = 6 t - 2 t^{2}$
$\frac{d v}{d t} = 6 - 4 t$ ;
For maximum velocity, $\frac{d v}{d t} = 0$
$∴ 6 - 4 t = 0$ or $t = \frac{3}{2} s$

Q. 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 ?

2s

3s

32​s

23​s