A block of mass 1 kg starts from rest at x = 0 and moves along the x-axis under the action of a force F = kt, where t is time and k = 1 Ns-1. The distance the block will travel in 6 seconds is

Question

A block of mass 1 kg starts from rest at x = 0 and moves along the x-axis under the action of a force F = kt, where t is time and k = 1 Ns-1. The distance the block will travel in 6 seconds is (A) 36 m (B) 72 m (C) 108 m (D) 18 m

Tardigrade Admin · Accepted Answer

From Newton's second law F=m a m=1 kg F=1 × a=(d v/d t) According to the question, F=k t=(d v/d t) d v=k t ⋅ d t Integration gives v =(k t2/2)=(d x/d t) x =(k t3/6)=(1 × 6 × 6 × 6/6) =36 m

Q. A block of mass $1 k g$ starts from rest at $x = 0$ and moves along the x-axis under the action of a force $F = k t$ , where $t$ is time and $k = 1 N s^{- 1}$ . The distance the block will travel in $6$ seconds is

36 m

72 m

108 m

18 m

From Newton's second law
$F = ma$
$m = 1 k g$
$F = 1 \times a = \frac{d v}{d t}$
According to the question,
$F = k t = \frac{d v}{d t}$
$d v = k t \cdot d t$
Integration gives
$v = \frac{k t ^{2}}{2} = \frac{d x}{d t}$
$x = \frac{k t ^{3}}{6} = \frac{1 \times 6 \times 6 \times 6}{6}$
$= 36 m$

Q. A block of mass 1kg starts from rest at x=0 and moves along the x-axis under the action of a force F=kt, where t is time and k=1Ns−1. The distance the block will travel in 6 seconds is