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A body of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $v=\mathrm{ax}^{3 / 2}$ where $\mathrm{a}=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$. What is the work done by the net force during its displacement from $x=0$ to $x=2$ m?
A body of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $v=\mathrm{ax}^{3 / 2}$ where $\mathrm{a}=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$. What is the work done by the net force during its displacement from $x=0$ to $x=2$ m?
CBSE | Class 11 | NCERT | Physics | Work, Energy, and Power
A body of mass $0.5 \mathrm{~kg}$ travels in a straight line with velocity $v=\mathrm{ax}^{3 / 2}$ where $\mathrm{a}=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$. What is the work done by the net force during its displacement from $x=0$ to $x=2$ m?

Let the mass of the body be $m$

$m=0.5 \mathrm{~kg}$

Velocity of the body is represented by $v=a x^{3 / 2}$

where,

$a=5 \mathrm{~m}^{-1 / 2} \mathrm{~s}^{-1}$.

Initial velocity at $x=0$ will be $v_{1}=a \times 0=0$

Final velocity at $x=2$ will be $v_{2}=a(2)^{3 / 2}=5 \times(2)^{3 / 2}$

Work done by the system=increase in K.E of the body

$=1 / 2 m\left(v_{2}^{2}-v_{1}^{2}\right)=1 / 2 \times 0.5\left[\left(5 \times(2)^{3 / 2}\right)^{2}-0\right]$

$=(1 / 2) \times 0.5 \times(25 \times 8)=50J$

i

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