Answer
Verified
450.9k+ views
Hint: We know that acceleration is how fast or slow the velocity is with respect to time.This differentiation is nothing but the slope of the graph. Hence we must take the slope of the given curves to find the correct option, among the following.
Formula used:
$a=\dfrac{dv}{dt}=\dfrac{d^{2}x}{dt^{2}}$
Complete answer:
We know that velocity is the rate of change of displacement with respect to time. It is mathematically denoted as $v=\dfrac{dx}{dt}$. This is nothing but the slope of the x-t graph.
Similarly, acceleration is the rate of change of velocity with respect to time. It is mathematically denoted as $a=\dfrac{dv}{dt}$. This is nothing but the slope of the v-t graph.
Given that acceleration is zero, or $a=\dfrac{dv}{dt}=0$, this happens when velocity is a constant . i.e. velocity is independent of time and its slope is $0$.
Since we know from mathematics, that $\dfrac{d}{dx}k=0$
Then the v-t graph is given as:
Then for $v$ to be a constant with respect to time we can say that the x-t graph is linear. Like $k\times x$ this is because we know that $\dfrac{d}{dx}kx=k$.
Since the x-t graph must be linear, in the given options, only C is linear and the other options are not linear i.e. specifically quadratic here.
So, the correct answer is “Option C”.
Note:
Here, the answer is discussed in the form of derivation of simplicity. However one can integrate $a=\dfrac{dv}{dt}=0$ twice, to reach the same answer. It is important to know either integration or differentiation to solve this sum. Also note that the slope of the x-t graph is nothing but the velocity and the slope of the v-t graph is the acceleration.
Formula used:
$a=\dfrac{dv}{dt}=\dfrac{d^{2}x}{dt^{2}}$
Complete answer:
We know that velocity is the rate of change of displacement with respect to time. It is mathematically denoted as $v=\dfrac{dx}{dt}$. This is nothing but the slope of the x-t graph.
Similarly, acceleration is the rate of change of velocity with respect to time. It is mathematically denoted as $a=\dfrac{dv}{dt}$. This is nothing but the slope of the v-t graph.
Given that acceleration is zero, or $a=\dfrac{dv}{dt}=0$, this happens when velocity is a constant . i.e. velocity is independent of time and its slope is $0$.
Since we know from mathematics, that $\dfrac{d}{dx}k=0$
Then the v-t graph is given as:
Then for $v$ to be a constant with respect to time we can say that the x-t graph is linear. Like $k\times x$ this is because we know that $\dfrac{d}{dx}kx=k$.
Since the x-t graph must be linear, in the given options, only C is linear and the other options are not linear i.e. specifically quadratic here.
So, the correct answer is “Option C”.
Note:
Here, the answer is discussed in the form of derivation of simplicity. However one can integrate $a=\dfrac{dv}{dt}=0$ twice, to reach the same answer. It is important to know either integration or differentiation to solve this sum. Also note that the slope of the x-t graph is nothing but the velocity and the slope of the v-t graph is the acceleration.
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
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
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