SATHEE: Kinematics 4 Question 2

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)

Analytical & Descriptive Questions

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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

$∴$ Displacement of particle $=$ Area of triangle $O P A +$ Area of square $P A B S P +$ Area of rectangle $Q B C R Q$

$\begin{aligned} = \frac{1}{2} \times 2 \times 2 + (2 \times 2) + (3 \times 1) \\ = 2 + 4 + 3 = 9 m \end{aligned}$

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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=5s ?

Analytical & Descriptive Questions

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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 $t = 5 s$ ?