Question

The displacement $x$ of a particle of mass $m\text{kg}$ moving in one dimension is related to the time $t$ by the equation $t=4x+3$ where $x$ is in metre and $t$ is in second. The work done by the force in the first six seconds in joules is

• A. $0\text{J}$
• B. $3\text{J}$
• C. $6\text{J}$
• D. $9\text{J}$

Answer 1

The correct option is A $0\text{J}$

Given,
$t=4x+3\Rightarrow x=\frac{1}{4}(t-3)$
$v=\frac{dx}{dt}=\frac{1}{4}\left(1\right)=\frac{1}{4}\text{m}/\text{s}$
So, the velocity is constant.

According to Work energy theorem,
$W_{net}=\Delta KE=0$