Question

Figure gives the acceleration of a $2.0kg$ body as it moves from rest along $x$ axis while a variable force acts on it from $x=0m$ to $x=9m$. The work done by the force on the body when it reaches
(i) $x=4m$ and
(ii) $x=7m$ shall be as given below

• A. $21J$ and $33J$ respectively
• B. $21J$ and $15J$ respectively
• C. $42J$ and $60J$ respectively
• D. $42J$ and $30J$ respectively

Answer 1

The correct option is D $42J$ and $30J$ respectively

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We know,

$W=\int F.dx=m\int a.dx$

$\int a.dx$= Algebraic sum of Area under a-x curve.

At $x=4m$

Area=21, Work done=42J

At $x=7m$

Area=15, Work done=30J

Option $\text{D}$ is the correct answer