
At time $t = {t_1}$ an object’s velocity is given by the vector $\overrightarrow {{v_1}} $ shown below.
$ \to $
A short time later, at $t = {t_2}$, the object’s velocity is the vector $\overrightarrow {{v_2}} $
$ \nearrow $
If $\overrightarrow {{v_1}} $ and $\overrightarrow {{v_2}} $ have the same magnitude, which one of the following vectors best illustrates the object’s average acceleration between $t = {t_1}$ and $t = {t_2}$?
(A)

(B)

(C)

(D)

(E)

Answer
125.7k+ views
Hint: Since the magnitudes of the vectors are the same so we need to only consider their direction. In order to calculate the acceleration, the direction of the first vector must be reversed to represent the difference.
Complete step by step answer
The basic difference between scalars and vectors is that scalar quantities just represent the magnitude whereas the vector represents both the direction and magnitude of the quantity.
For example, mass of a body does not have any particular direction but it does have a magnitude to represent the quantity. These types of quantities are called scalar quantities. On the other hand, the force acting on a body can be represented by both direction and magnitude. When we push someone or something, we are exerting some amount of force in a particular direction. These quantities are called vectors.
Vectors are usually denoted by drawing an arrow just above the sign representing the quantity.
In this question we need to find the resultant of two vectors.
We are given the velocity vectors at time ${t_1}$ and ${t_2}$
Now, acceleration is defined as the rate of change of velocity
So, $\overrightarrow a = \dfrac{{\overrightarrow {{v_2}} - \overrightarrow {{v_1}} }}{{{t_2} - {t_1}}}$
Now, the resultant of vectors $\overrightarrow {{v_1}} $ and $\overrightarrow {{v_2}} $results in option A. Since we need to find their difference, we can assume that the direction of vector $\overrightarrow {{v_1}} $ is reversed.
If this direction is reversed then their resultant vector would be correctly represented by option C.
Therefore, the correct option is C.
Note: Unlike scalar quantities, vectors have two types of product. Dot and cross. Dot product tells us how much of two vectors are in the same direction whereas the cross product tells us how little the two vectors are in the same direction. Dot product of two vectors gives us a scalar quantity, while the cross product of two vectors gives us a vector quantity.
Complete step by step answer
The basic difference between scalars and vectors is that scalar quantities just represent the magnitude whereas the vector represents both the direction and magnitude of the quantity.
For example, mass of a body does not have any particular direction but it does have a magnitude to represent the quantity. These types of quantities are called scalar quantities. On the other hand, the force acting on a body can be represented by both direction and magnitude. When we push someone or something, we are exerting some amount of force in a particular direction. These quantities are called vectors.
Vectors are usually denoted by drawing an arrow just above the sign representing the quantity.
In this question we need to find the resultant of two vectors.
We are given the velocity vectors at time ${t_1}$ and ${t_2}$
Now, acceleration is defined as the rate of change of velocity
So, $\overrightarrow a = \dfrac{{\overrightarrow {{v_2}} - \overrightarrow {{v_1}} }}{{{t_2} - {t_1}}}$
Now, the resultant of vectors $\overrightarrow {{v_1}} $ and $\overrightarrow {{v_2}} $results in option A. Since we need to find their difference, we can assume that the direction of vector $\overrightarrow {{v_1}} $ is reversed.
If this direction is reversed then their resultant vector would be correctly represented by option C.
Therefore, the correct option is C.
Note: Unlike scalar quantities, vectors have two types of product. Dot and cross. Dot product tells us how much of two vectors are in the same direction whereas the cross product tells us how little the two vectors are in the same direction. Dot product of two vectors gives us a scalar quantity, while the cross product of two vectors gives us a vector quantity.
Recently Updated Pages
JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

JEE General Topics in Chemistry Important Concepts and Tips

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility & More

Class 11 JEE Main Physics Mock Test 2025

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

JEE Main 2023 January 24 Shift 2 Question Paper with Answer Keys & Solutions

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Fluids

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
