# Fundamentals of Physics Chapter 4 Solutions: Motion in Two and Three Dimensions

Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions for Chapter 4 ‘Motion in Two and Three Dimensions’ will help you prepare for JEE. This chapter of Resnick Halliday Walker Solutions covers some important topics like position, displacement, average velocity, instantaneous velocity, acceleration, projectile motion, applications of projectile motion, equation of path, horizontal range, uniform circular motion, and relative motion in one dimension. After studying all these concepts, you will be able to determine the direction and the magnitude of a particle’s position, draw two-dimensional and three-dimensional velocity vectors for a particle and apply the constant acceleration equations to relate acceleration, velocity, position, and time.

Resnick Halliday & Walker Fundamentals of Physics Volume 1 ‘Motion in Two and Three Dimensions’ contains 138 questions in total. These questions have been put into 8 modules that cover all the topics of the chapter. After practising these questions, you will find that all questions have covered important concepts such as acceleration, velocity, displacement, circular motion, projectile motion, etc. This chapter is of great significance for your competitive exams like IIT JEE or NEET. To score well in exams, you must study all the questions.

Instasolv gives you the answers to all the questions provided in Motion in Two and Three Dimensions of Resnick Halliday and Walker Physics Volume 1. The experts at Instasolv are proficient and have prepared the authentic answers for your IIT JEE exam preparation. You will be able to comprehend our solutions easily because all the answers have been explained step by step by the professionals. Practising Instasolv’s solutions can also help you with some tricks to save a lot of time during competitive exams.

## Important Topics for Halliday Resnick & Walker Fundamentals of Physics Volume 1 Solutions Chapter 4: Motion in Two and Three Dimensions

**Displacement:** Displacement is defined as the shortest distance covered by an object. During the object’s movement, the position vector also changes from r1 to r2, then the displacement is calculated by

Δr=r_{2} – r_{1}

**Average Velocity:** When a particle experiences a displacement r in time interval t, then its average velocity for that time interval is calculated by

**Instantaneous Velocity: **It is the velocity of an object in motion at a specific point in time when the time period approaches zero. After approaching zero, v_{avg}. reaches a limit which is then called instantaneous velocity. It is calculated by

v= dr/dt

In unit-vector notation, it is calculated as

v_{x} = dx/dt, v_{y} = dy/dt, and v_{z} = dz/dt.

The instantaneous velocity of a particle is always directed along the tangent to the particle’s path at the particle’s position.

**Average Acceleration:** You can find the average acceleration of a particle by subtracting its final velocity with the initial velocity per time taken.

a_{avg}= Δv ⁄ Δt

**Instantaneous Acceleration: **If you shrunk the change in time to 0, then a_{avg}. reaches a limiting value which is called instantaneous acceleration. This can be calculated by using differentiation.

a=dv/dt

Similarly, you can calculate instantaneous acceleration in unit vector notation.

**Projectile Motion:** It is a kind of motion that an object experiences when it is projected near the Earth’s surface which makes it move along a curved path under the action of gravity.

- During the flight of this particle, it’s horizontal acceleration is zero.
- Its vertical acceleration is taken -g because it moves opposite from the gravity.
- The trajectory of an object is its path covered in projectile motion which is parabolic.

**Uniform Circular Motion:** When an object travels along a circular path or circular arc of radius r at a constant speed of v, then it is said to be in uniform circular motion and possess an acceleration of constant magnitude.

a=v^{2}/r

The time taken by the object to complete a circle is given by

**Relative Motion: **It is a type of motion that is observed by the observer and is dependent on the location (frame) of the observer.

### Exercise Discussion of Resnick Halliday and Walker Fundamentals of Physics Volume 1 Solutions Chapter 4: Motion in Two and Three Dimensions

**Module 1: Position and displacement **

This module covers only 4 questions based on position and displacement where you have to find the magnitude and angle of displacement, the position of the initial position vector, and write unit vector notations.

**Module 2: Average velocity and instantaneous velocity **

In this module, you will find 6 questions that ask you to find an average and instantaneous velocity of an object. You will also find some graphical questions here.

**Module 3: Average acceleration and instantaneous acceleration**

Here you will find 9 questions based on this topic. You have to find the angle between the tangent to a particle’s path and the x-axis, magnitude of a vector, and time when velocity is zero.

**Module 4: Projectile motion **

This module contains 37 questions based on projectile motion. These questions ask you to find speed, acceleration, time, distance, the magnitude of horizontal or vertical components, etc. of an object during projectile motion.

**Module 5**: **Uniform circular motion**

This module covers 12 questions that ask you to find the magnitude, direction, velocity, acceleration, time, etc, of an object when it moves in a circular motion.

**Module 6: Relative motion in one dimension **

Here you will find only 3 questions based on finding the acceleration of an object, magnitude of acceleration, and direction of acceleration.

**Module 7: Relative motion in two dimension**

This Resnick Halliday module contains 10 questions. You have to find the angle between the line of sights, provide the speed of one object with respect to another, relative speed, and magnitude and direction of velocity.

**Module 8: Additional questions **

This module has a total no. of 45 questions that cover all the concepts provided in the chapter. All these questions are of a slightly higher order thinking level.

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