Work Power and Energy 5 Question 4
6. A block of mass $2 kg$ is free to move along the $x$-axis. It is at rest and from $t=0$ onwards it is subjected to a time-dependent force $F(t)$ in the $x$-direction. The force $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5 s$ is
(2010)
(a) $4.50 J$
(b) $7.50 J$
(c) $5.06 J$
(d) $14.06 J$
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Answer:
Correct Answer: 6. (c)
Solution:
- Area under $F-t$ graph $=$ momentum $=p=\sqrt{2 km}$
$$ \begin{aligned} \therefore \quad k & =\frac{A^{2}}{2 m} \quad(A=\text { net area of } F-t \text { graph }) \\ & =\frac{\frac{4 \times 3}{2}-\frac{1.5 \times 2}{2}{ }^{2}}{2 \times 2} \\ & =5.0625 J \end{aligned} $$
