
The velocity n m/s of a particle is proportional to the cube of the time. If the velocity after 2s is 4m/s, then n is equal to:
(A) ${t^3}\;$
(B) $\dfrac{{{t^3}\;}}{2}$
(C) $\dfrac{{{t^3}\;}}{3}$
(D) $\dfrac{{{t^3}\;}}{4}$
Answer
153.9k+ views
Hint It should be known to us that velocity is defined as the rate of change of the position of an object with respect to the frame of reference of the time. Based on this concept we have to solve this question.
Complete step by step answer
The velocity of a particle is given as n m/s and it is proportional to the cube of the time.
Given that the velocity becomes 4m/s after 2 seconds,
We can derive that,
$n{\text{ }}\propto {\text{ }}{\left[ {Time\left( t \right)} \right]^3}$
Therefore, we can say that,
$n = k{t^3} \ldots \ldots \ldots \left( {\text{i}} \right)$
When velocity after 2 seconds become 4m/s,
We can equate,
$4 = k{\left( 2 \right)^3} \ldots \ldots \ldots \left( {{\text{ii}}} \right)$
$\Rightarrow 4 = 8k$
$\Rightarrow k = \dfrac{1}{2}$
Hence, we can derive n from the above equations as
${\text{n = }}\dfrac{{{{\text{t}}^{\text{3}}}}}{{\text{2}}}$ (from equation i)
Therefore, the correct answer is Option B.
Note To find the velocity we should always remember that we have to divide the change in the position by the change in time. Since it is a vector quantity we have to mention the direction as well.
Complete step by step answer
The velocity of a particle is given as n m/s and it is proportional to the cube of the time.
Given that the velocity becomes 4m/s after 2 seconds,
We can derive that,
$n{\text{ }}\propto {\text{ }}{\left[ {Time\left( t \right)} \right]^3}$
Therefore, we can say that,
$n = k{t^3} \ldots \ldots \ldots \left( {\text{i}} \right)$
When velocity after 2 seconds become 4m/s,
We can equate,
$4 = k{\left( 2 \right)^3} \ldots \ldots \ldots \left( {{\text{ii}}} \right)$
$\Rightarrow 4 = 8k$
$\Rightarrow k = \dfrac{1}{2}$
Hence, we can derive n from the above equations as
${\text{n = }}\dfrac{{{{\text{t}}^{\text{3}}}}}{{\text{2}}}$ (from equation i)
Therefore, the correct answer is Option B.
Note To find the velocity we should always remember that we have to divide the change in the position by the change in time. Since it is a vector quantity we have to mention the direction as well.
Recently Updated Pages
JEE Main 2022 (June 29th Shift 2) Maths Question Paper with Answer Key

JEE Main 2023 (January 25th Shift 1) Maths Question Paper with Answer Key

JEE Main 2022 (July 29th Shift 1) Maths Question Paper with Answer Key

JEE Main 2022 (July 26th Shift 2) Chemistry Question Paper with Answer Key

JEE Main 2022 (June 26th Shift 2) Maths Question Paper with Answer Key

JEE Main 2022 (June 29th Shift 1) Physics Question Paper with Answer Key

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

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Degree of Dissociation and Its Formula With Solved Example for JEE

Displacement-Time Graph and Velocity-Time Graph for JEE

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

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

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

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