Acceleration Vs. Displacement Graph

[manfriction]

I Have a question

If acceleration(a)=Displacement(x)
and at time(t)=0 if Velocity(u) is 0
then we have to find velocity at time=2 secs

Attempt At Answer
given: a=x
or v dv = x dx
integrating both sides with initial velocity 0 and displ. s
v2=x2-s2
or
v=√(x2-s2)
or
dx/√(x2-s2)=dt
integrating again
we get
(x/s)=cos t

but the problem is how do we get value of initial displ. s??
if we ignore s
we get
x=e^t
but the graph of this gives x=1 at t=o so we can't ignore "s"

Plz help..

 

[HallsofIvy]

"displacement" is the distance moved- not just the final position. Take initial s to be anything you like since you would just subtract it off anyway. s= 0 is easiest.

 

[Moetasim]

Thank you for your question. The acceleration vs. displacement graph shows the relationship between acceleration and displacement over time. It can be a useful tool for understanding the motion of an object.

In order to find the velocity at time = 2 seconds, we need to know the initial displacement (s) of the object. This is because the equation v = √(x^2 - s^2) includes the initial displacement in its calculation. Without knowing the value of s, we cannot accurately determine the velocity at a specific time.

One way to find the initial displacement is to use the information given in the problem. We know that at time t = 0, the velocity (u) is 0. This means that the object is at rest at this time, and therefore its displacement (s) must be 0 as well. With this information, we can now accurately calculate the velocity at time t = 2 seconds.

I hope this helps. If you have any further questions, please let me know.