SATHEE: Motion in a Plane - Result Question 4

Motion in a Plane - Result Question 4

4. A particle is moving such that its position coordinate $(x, y)$ are

$(2 m, 3 m)$ at time $t = 0$

$(6 m, 7 m)$ at time $t = 2 s$ and

$(13 m, 14 m)$ at time $t = 5 s$ .

Average velocity vector $({\vec{V}}_{a v})$ from $t = 0$ to $t = 5 s$ is :

[2014]

(a) $\frac{1}{5} (13 \hat{i} + 14 \hat{j})$

(b) $\frac{7}{3} (\hat{i} + \hat{j})$

(d) $\frac{11}{5} (\hat{i} + \hat{j})$

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Answer:

Correct Answer: 4. (d)

Solution:

(d) ${\vec{v}}_{a v} = \frac{Δ \vec{r} (displacement)}{Δ t (time taken)}$

$= \frac{(13 - 2) \hat{i} + (14 - 3) \hat{j}}{5 - 0} = \frac{11}{5} (\hat{i} + \hat{j})$ When a point have coordinate $(x, y)$ then its position vector $= x \hat{i} + y \hat{j}$

When a particle moves from point $(x_{1}, y_{1})$ to $(x_{2}, y_{2})$ then its displacement vector

$\vec{r} = (x_{2} - x_{1}) \hat{i} + (y_{2} - y_{1}) \hat{j}$

Motion in a Plane - Result Question 4

4. A particle is moving such that its position coordinate $(x, y)$ are

Answer:

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Motion in a Plane - Result Question 4

4. A particle is moving such that its position coordinate (x,y) are

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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4. A particle is moving such that its position coordinate $(x, y)$ are