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:
- 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 $=\Delta k=4.5 J$
