Answer
Verified
425.4k+ views
Hint Since the acceleration is constant with time so the velocity is increasing at a constant rate. Thus from there we can draw the v-t graph. From the equation of motion we can see that the equation for position is quadratic in time so the graph will be parabolic.
Formula Used: In this solution we will be using the following formula,
$\Rightarrow x = ut + \dfrac{1}{2}a{t^2} $
where $ x $ is the position, $ u $ is the initial velocity, $ a $ is the acceleration and $ t $ is the time.
Complete step by step answer
In the question we are given the graph of the acceleration with respect to time. In the graph we can see that it is a straight line which is parallel to the time axis. This means that the acceleration remains constant with time.
Now for a velocity time graph, the slope is given by $ \dfrac{{dv}}{{dt}} $ . Now the differentiation of velocity with respect to time gives us the acceleration. So we can write,
$\Rightarrow \dfrac{{dv}}{{dt}} = a $
On integrating we get,
$\Rightarrow v = u + at $
where the initial velocity can be taken as $ u = 0 $ for time 0. Hence we see that the velocity is directly proportional to the time. So the graph will be a straight line passing through the origin for $ u = 0 $ .
That is,
Now for the position time graph, again, the acceleration is the double differentiation of the position. So we can write,
$\Rightarrow \dfrac{{{d^2}x}}{{d{t^2}}} = a $
On integrating twice we get,
$\Rightarrow x = ut + \dfrac{1}{2}a{t^2} $
If the initial velocity is considered to be zero, for time zero, we get,
$\Rightarrow x = \dfrac{1}{2}a{t^2} $
From here we can see that the position is a quadratic equation of time and represents the form of a parabola. So the graphical representation will be,
Note
Using the velocity time graph we can find both the acceleration and the displacement of the particle. The slope of the velocity time graph given the acceleration and the area covered under the velocity time graph gives the displacement of the particle.
Formula Used: In this solution we will be using the following formula,
$\Rightarrow x = ut + \dfrac{1}{2}a{t^2} $
where $ x $ is the position, $ u $ is the initial velocity, $ a $ is the acceleration and $ t $ is the time.
Complete step by step answer
In the question we are given the graph of the acceleration with respect to time. In the graph we can see that it is a straight line which is parallel to the time axis. This means that the acceleration remains constant with time.
Now for a velocity time graph, the slope is given by $ \dfrac{{dv}}{{dt}} $ . Now the differentiation of velocity with respect to time gives us the acceleration. So we can write,
$\Rightarrow \dfrac{{dv}}{{dt}} = a $
On integrating we get,
$\Rightarrow v = u + at $
where the initial velocity can be taken as $ u = 0 $ for time 0. Hence we see that the velocity is directly proportional to the time. So the graph will be a straight line passing through the origin for $ u = 0 $ .
That is,
Now for the position time graph, again, the acceleration is the double differentiation of the position. So we can write,
$\Rightarrow \dfrac{{{d^2}x}}{{d{t^2}}} = a $
On integrating twice we get,
$\Rightarrow x = ut + \dfrac{1}{2}a{t^2} $
If the initial velocity is considered to be zero, for time zero, we get,
$\Rightarrow x = \dfrac{1}{2}a{t^2} $
From here we can see that the position is a quadratic equation of time and represents the form of a parabola. So the graphical representation will be,
Note
Using the velocity time graph we can find both the acceleration and the displacement of the particle. The slope of the velocity time graph given the acceleration and the area covered under the velocity time graph gives the displacement of the particle.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE