How to Draw an Acceleration vs Displacement Graph?

[hav0c]

Homework Statement

The graph is as folllows-(SEE ATTACHMENT)
Q.draw acceleration vs disp. graph.

Homework Equations

Basic equations of motion, basic calculus

The Attempt at a Solution

I have tried to write a linear equation in v and s and then differentiating it w.r.t. to time. but I am not sure if this is the correct way to do it. It gives me a positive slope and -ve y intercept.
Also if there is/are any other ways please do tell

 

[darkxponent]

first write the v-s equation, but do not diffrentiate it with time(as it would add one more variable which is not needed)

Hint: What is the relation between v,a and s?

 

[hav0c]

thanks for your reply.
i have solved the question.
1 doubt though which extra variable is generated? on differentiation
v becomes a
s becomes v
constant is eliminated

 

[darkxponent]

thanks for your reply.
i have solved the question.
1 doubt though which extra variable is generated? on differentiation
v becomes a
s becomes v
constant is eliminated

I thought 't" would create some some problems but thanks it is eliminated. You can also do it using the relation a = v*dv/ds. This was what i was referring to!

 

[Nickie]

me.I would approach this problem by first understanding the relationship between velocity and displacement. The velocity vs displacement graph shows the relationship between these two variables, where velocity is plotted on the y-axis and displacement is plotted on the x-axis.

To draw the acceleration vs displacement graph, we need to understand the relationship between acceleration, velocity, and displacement. Acceleration is defined as the rate of change of velocity with respect to time, and it can be calculated by taking the derivative of the velocity function. Therefore, to draw the acceleration vs displacement graph, we need to take the derivative of the velocity function and plot it on the y-axis, while displacement remains on the x-axis.

One way to approach this is to use the basic equations of motion, specifically the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging this equation, we get a = (v-u)/t. We can then substitute the equation for velocity (v = ds/dt) into this equation, where s is the displacement and t is the time. This gives us a = (ds/dt - u)/t.

Therefore, the equation for acceleration as a function of displacement is a = (ds/dt - u)/t. To plot this on the graph, we can choose different values for u and t and use the equation to calculate the corresponding values of acceleration. This will give us a series of points that we can then plot on the acceleration vs displacement graph.

Another approach could be to use basic calculus to find the derivative of the velocity function, which will give us the acceleration function. We can then plot this function on the graph to get the acceleration vs displacement curve.

In conclusion, there are several ways to approach this problem, but the key is to understand the relationship between velocity, acceleration, and displacement and use the appropriate equations and methods to calculate and plot the acceleration vs displacement graph.