
The velocity of a body depends on time according to the equation v = 20 + 0.1${{t}^{2}}$. The body is undergoing
A. uniform acceleration
B. uniform retardation
C. non- uniform acceleration
D. zero acceleration
Answer
164.4k+ views
Hint: In this question, we are given the velocity and we have to find out in which acceleration body is going. We know the rate of change of velocity is acceleration. So first we differentiate the given equation and then with the help of relation of acceleration and time we find out in which acceleration the body is going and choose the option accordingly.
Formula used:
We use the formula of velocity:-
\[\text{velocity}=\dfrac{\text{change in displacement}}{\text{time taken}}\]
Complete step by step solution:
Velocity is the rate of change of displacement of a body.
\[\text{velocity}=\dfrac{\text{change in displacement}}{\text{time taken}} \\ \]
And the rate of change of velocity is called the acceleration of the body.
$a=\dfrac{{{v}_{2}}-{{v}_{1}}}{{{t}_{2}}-{{t}_{1}}} \\ $
That is $a=\dfrac{dv}{dt} \\ $
Given v = 20 + 0.1${{t}^{2}} \\ $
We know acceleration is differentiating velocity with time.
That is a = $\dfrac{dv}{dt} \\ $
Then a = $\dfrac{d(20+0.1{{t}^{2}})}{dt} \\ $
$\therefore a = 0.2 t$
From the above, it is clear that acceleration depends upon the time or we say that the speed of the particle changes by time. So, it is a non- uniform acceleration.
Thus, option C is the correct answer.
Note: If the body is under uniform acceleration, then there will be constant acceleration with changes in time. If the acceleration depends on time, then the acceleration increases with increase in time or it will decrease with the decrease in time.
Formula used:
We use the formula of velocity:-
\[\text{velocity}=\dfrac{\text{change in displacement}}{\text{time taken}}\]
Complete step by step solution:
Velocity is the rate of change of displacement of a body.
\[\text{velocity}=\dfrac{\text{change in displacement}}{\text{time taken}} \\ \]
And the rate of change of velocity is called the acceleration of the body.
$a=\dfrac{{{v}_{2}}-{{v}_{1}}}{{{t}_{2}}-{{t}_{1}}} \\ $
That is $a=\dfrac{dv}{dt} \\ $
Given v = 20 + 0.1${{t}^{2}} \\ $
We know acceleration is differentiating velocity with time.
That is a = $\dfrac{dv}{dt} \\ $
Then a = $\dfrac{d(20+0.1{{t}^{2}})}{dt} \\ $
$\therefore a = 0.2 t$
From the above, it is clear that acceleration depends upon the time or we say that the speed of the particle changes by time. So, it is a non- uniform acceleration.
Thus, option C is the correct answer.
Note: If the body is under uniform acceleration, then there will be constant acceleration with changes in time. If the acceleration depends on time, then the acceleration increases with increase in time or it will decrease with the decrease in time.
Recently Updated Pages
How to Calculate Moment of Inertia: Step-by-Step Guide & Formulas

Dimensions of Charge: Dimensional Formula, Derivation, SI Units & Examples

Dimensions of Pressure in Physics: Formula, Derivation & SI Unit

Environmental Chemistry Chapter for JEE Main Chemistry

Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

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

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

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

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

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

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

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

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

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