A block of mass 2 kg is having velocity 4√5 m s- 1 in the positive x-direction at the origin. The only force acting on it is F=(3 x2 - 12 x) N . Its velocity when it is at x=2 m is

Question

A block of mass 2 kg is having velocity 4√5 m s- 1 in the positive x-direction at the origin. The only force acting on it is F=(3 x2 - 12 x) N . Its velocity when it is at x=2 m is (A) 8 m s- 1 (B) 4 ms- 1 (C) 10√24 m s- 1 (D) 20 ms- 1

Tardigrade Admin · Accepted Answer

From work energy theorem W=Δ K displaystyle ∫ 02 F d x = (1/2) m (v2 - u2) displaystyle ∫ 02 (3 x2 - 12 x) d x = (1/2) 2 (v2 - (4 √5)2) [x3 - 6 x2]02=v2-80 8-24+80=v2 v=8 m s- 1

Q. A block of mass $2 k g$ is having velocity $45 m s^{- 1}$ in the positive x-direction at the origin. The only force acting on it is $F = (3 x^{2} - 12 x) N$ . Its velocity when it is at $x = 2 m$ is

$8 m s^{- 1}$

$4 m s^{- 1}$

$1024 m s^{- 1}$

$20 m s^{- 1}$

From work energy theorem
$W = Δ K$
$\int_{0}^{2} F d x = \frac{1}{2} m (v^{2} - u^{2})$
$\int_{0}^{2} (3 x^{2} - 12 x) d x = \frac{1}{2} 2 (v^{2} - (45)^{2})$
$[x^{3} - 6 x^{2}]_{0}^{2} = v^{2} - 80$
$8 - 24 + 80 = v^{2}$
$v = 8 m s^{- 1}$

Q. A block of mass 2kg is having velocity 45​ms−1 in the positive x-direction at the origin. The only force acting on it is F=(3x2−12x)N . Its velocity when it is at x=2m is

8ms−1

4ms−1

1024​ms−1

20ms−1