Kinematics 4 Question 2
2. A particle starts from the origin at time $t=0$ and moves along the positive $X$-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t=5 s$ ?
(2019 Main, 10 Jan II)
(a) 6 m
(b) 3 m
(c) 10 m
(d) 9 m
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Answer:
Correct Answer: 2. (d)
Solution:
- Key Idea
Area under the velocity-time curve represents displacement.
To get exact position at $t=5 s$, we need to calculate area of the shaded part in the curve as shown below
$\therefore$ Displacement of particle $=$ Area of triangle $O P A+$ Area of square $P A B S P+$ Area of rectangle $Q B C R Q$
$$ \begin{aligned} & =\frac{1}{2} \times 2 \times 2+(2 \times 2)+(3 \times 1) \\ & =2+4+3=9 m \end{aligned} $$
