Work Power and Energy 5 Question 2

4. A time dependent force $F=6 t$ acts on a particle of mass $1 kg$. If the particle starts from rest, the work done by the force during the first $1 s$ will be

(a) $22 J$

(b) $9 J$

(c) $18 J$

(d) $4.5 J$

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Answer:

Correct Answer: 4. (d)

Solution:

  1. From Newton’s second law, $\frac{\Delta p}{\Delta t}=F$

$\Rightarrow \Delta p=F \Delta t$

$\therefore \quad p=\int d p=\int _0^{1} F d t$

$\Rightarrow p=\int _0^{1} 6 t d t=3 \mathbf{k g} \frac{\mathbf{m}}{\mathbf{s}}$

Also, $\Delta k=\frac{\Delta p^{2}}{2 m}=\frac{3^{2}}{2 \times 1}=4.5$

So, work done $=\Delta k=4.5 J$



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