Q: Define position vector in a plane.

Position vector $\vec{r}$ of a particle at $(x,y)$ is given by $\vec{r}=x\hat{i}+y\hat{j}$ with respect to the origin $O(0,0)$.

Q: Define displacement vector.

Displacement vector is the change in position: $\Delta\vec{r}=\vec{r}_2-\vec{r}_1$, independent of the actual path followed.

Q: Write the expressions for average velocity in a plane.

Average velocity is $\vec{v}_{\text{avg}}=\frac{\Delta\vec{r}}{\Delta t}$, where $\Delta\vec{r}$ is displacement in time interval $\Delta t$.

Q: What is instantaneous velocity in 2D?

Instantaneous velocity is $\vec{v}=\frac{d\vec{r}}{dt}$ and is always tangent to the path at that instant.

Q: Define average acceleration in a plane.

Average acceleration is $\vec{a}_{\text{avg}}=\frac{\Delta\vec{v}}{\Delta t}$, where $\Delta\vec{v}$ is change in velocity in time $\Delta t$.

Q: What is instantaneous acceleration in a plane?

Instantaneous acceleration is $\vec{a}=\frac{d\vec{v}}{dt}$ and measures the rate of change of velocity vector at a given instant.

Question 1

What is motion in a plane?

Accepted Answer

Motion in a plane is motion of a particle in two dimensions, where its position, velocity, and acceleration are represented by vectors in an $x\text{-}y$ plane.

Question 2

What is a scalar quantity?

Accepted Answer

A scalar quantity is one that has only magnitude and no direction, such as mass, distance, speed, time, or temperature.

Question 3

What is a vector quantity?

Accepted Answer

A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, and force.

Question 4

Define position vector in a plane.

Accepted Answer

Position vector $\vec{r}$ of a particle at $(x,y)$ is given by $\vec{r}=x\hat{i}+y\hat{j}$ with respect to the origin $O(0,0)$.

Question 5

Define displacement vector.

Accepted Answer

Displacement vector is the change in position: $\Delta\vec{r}=\vec{r}_2-\vec{r}_1$, independent of the actual path followed.

Question 6

Write the expressions for average velocity in a plane.

Accepted Answer

Average velocity is $\vec{v}_{\text{avg}}=\frac{\Delta\vec{r}}{\Delta t}$, where $\Delta\vec{r}$ is displacement in time interval $\Delta t$.

Question 7

What is instantaneous velocity in 2D?

Accepted Answer

Instantaneous velocity is $\vec{v}=\frac{d\vec{r}}{dt}$ and is always tangent to the path at that instant.

Question 8

Define average acceleration in a plane.

Accepted Answer

Average acceleration is $\vec{a}_{\text{avg}}=\frac{\Delta\vec{v}}{\Delta t}$, where $\Delta\vec{v}$ is change in velocity in time $\Delta t$.

Question 9

What is instantaneous acceleration in a plane?

Accepted Answer

Instantaneous acceleration is $\vec{a}=\frac{d\vec{v}}{dt}$ and measures the rate of change of velocity vector at a given instant.

Question 10

State the triangle law of vector addition.

Accepted Answer

If two vectors are represented by two sides of a triangle taken in order, the third side taken in the same order represents their resultant.

Question 11

State the parallelogram law of vector addition.

Accepted Answer

If two vectors from the same point form adjacent sides of a parallelogram, the diagonal through that point gives the resultant vector.

Question 12

Give formula for magnitude of resultant of two vectors.

Accepted Answer

For vectors $\vec{A}$ and $\vec{B}$ with angle $\theta$ between them, resultant magnitude is $R=\sqrt{A^2+B^2+2AB\cos\theta}$.

Question 13

What is vector subtraction?

Accepted Answer

Vector subtraction $\vec{A}-\vec{B}$ is defined as $\vec{A}+(-\vec{B})$, where $-\vec{B}$ has same magnitude as $\vec{B}$ but opposite direction.

Question 14

What is a unit vector?

Accepted Answer

A unit vector has magnitude 1 and gives only direction; unit vector along $\vec{A}$ is $\hat{A}=\frac{\vec{A}}{|\vec{A}|}$

Question 15

Give components of a vector in a plane.

Accepted Answer

If $\vec{A}$ makes angle $\theta$ with positive $x$-axis, then $A_x=A\cos\theta$, $A_y=A\sin\theta$, and $\vec{A}=A_x\hat{i}+A_y\hat{j}$.

Quantity	Formula	Remarks
Resultant Magnitude	\(R = \sqrt{A^2+B^2+2AB\cos\theta}\)	Parallelogram law
Resultant Angle	\(\tan\phi = \frac{B\sin\theta}{A+B\cos\theta}\)	Angle with A
Max Height	\(H = \frac{u^2\sin^2\theta}{2g}\)	Projectile
Time of Flight	\(T = \frac{2u\sin\theta}{g}\)	Projectile
Range	\(R = \frac{u^2\sin 2\theta}{g}\)	R_max at θ=45°
Centripetal Acc.	\(a_c = \frac{v^2}{r} = \omega^2 r\)	Uniform circular motion
Angular Velocity	\(v = r\omega\)	Relation to linear speed
Period	\(T = \frac{2\pi r}{v} = \frac{2\pi}{\omega}\)	Circular motion

Motion in a Plane

Core Topics at a Glance

Key Formulae

All Resources for This Chapter

Important Points to Remember

Exam Corner

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