Answer
425.4k+ views
Hint: Acceleration is defined as the rate of change of speed with time. Any change in the velocity of an object will cause an acceleration. Increasing speed is what we usually mean when it is said as acceleration, decreasing speed which is also called deceleration or retardation, or changing direction known as centripetal acceleration.
Complete step by step answer:
First of all let us take a look at what actually the uniform acceleration means. If an object's speed or velocity is increasing at a constant rate then we can say that it has uniform acceleration. The rate of acceleration is similar. If a car speeds up then slows down then speeds up then we can assume that car is not having a uniform acceleration.
Here in this question, it is given that acceleration is constant or the body moves with a uniform acceleration. Therefore we write that,
Acceleration=a=constant.
Hence we can write that,
$dV=adt$
Let us integrate this,
$\begin{align}
& \int\limits_{u}^{v}{dv}=a\int\limits_{0}^{t}{dt} \\
& \left[ v \right]_{u}^{v}=a\left[ t \right]_{0}^{t} \\
\end{align}$
That means $S=\dfrac{1}{2}a{{t}^{2}}$
$\begin{align}
& \left[ v-u \right]=at \\
& v=u+at \\
\end{align}$
And also we know that,
$ds=vdt$
This should be integrated,
$\int\limits_{0}^{s}{ds=\int\limits_{0}^{t}{udt+a\int\limits_{0}^{t}{tdt}}}$
Integrating this will give,
$S=ut+\dfrac{1}{2}a{{t}^{2}}$
Therefore as per the relation obtained we can say that, the graph should be a parabola which should be symmetric about the x-axis.
Hence we can see that option A is the right one when
$u=0$
And then
$S=\dfrac{1}{2}a{{t}^{2}}$
So, the correct answer is “Option A”.
Note: A body with a velocity zero can still accelerate. The simplest example is an object which is thrown upwards. At the highest point its velocity will become zero but will still accelerate due to the acceleration of gravity. The direction of the acceleration will decide whether you should add (positive acceleration) or subtract (negative acceleration).
Complete step by step answer:
First of all let us take a look at what actually the uniform acceleration means. If an object's speed or velocity is increasing at a constant rate then we can say that it has uniform acceleration. The rate of acceleration is similar. If a car speeds up then slows down then speeds up then we can assume that car is not having a uniform acceleration.
Here in this question, it is given that acceleration is constant or the body moves with a uniform acceleration. Therefore we write that,
Acceleration=a=constant.
Hence we can write that,
$dV=adt$
Let us integrate this,
$\begin{align}
& \int\limits_{u}^{v}{dv}=a\int\limits_{0}^{t}{dt} \\
& \left[ v \right]_{u}^{v}=a\left[ t \right]_{0}^{t} \\
\end{align}$
That means $S=\dfrac{1}{2}a{{t}^{2}}$
$\begin{align}
& \left[ v-u \right]=at \\
& v=u+at \\
\end{align}$
And also we know that,
$ds=vdt$
This should be integrated,
$\int\limits_{0}^{s}{ds=\int\limits_{0}^{t}{udt+a\int\limits_{0}^{t}{tdt}}}$
Integrating this will give,
$S=ut+\dfrac{1}{2}a{{t}^{2}}$
Therefore as per the relation obtained we can say that, the graph should be a parabola which should be symmetric about the x-axis.
Hence we can see that option A is the right one when
$u=0$
And then
$S=\dfrac{1}{2}a{{t}^{2}}$
So, the correct answer is “Option A”.
Note: A body with a velocity zero can still accelerate. The simplest example is an object which is thrown upwards. At the highest point its velocity will become zero but will still accelerate due to the acceleration of gravity. The direction of the acceleration will decide whether you should add (positive acceleration) or subtract (negative acceleration).
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)