Acceleration in Kinematics: How Does it Vary with Displacement?

  • Thread starter Thread starter ritik.dutta3
  • Start date Start date
AI Thread Summary
The discussion centers on determining how acceleration varies with displacement for a particle described by the equation x = sqrt(at + 2bt + c). Participants express confusion over the problem's clarity and seek guidance on solving it. The solution involves taking the second derivative of the position function to find acceleration and using the chain rule to relate acceleration to displacement. A suggested method includes calculating dz/dx by deriving dz/dt and dx/dt, followed by substituting x back into the final result. The conversation emphasizes the importance of correctly interpreting the problem and applying calculus techniques.
ritik.dutta3
Messages
8
Reaction score
0

Homework Statement



A particle moves along a straight line such that its displacement x changes with time t as x= sqrt( at+2bt + c) where a, b and c are constants, then the acceleration varies with x as

Homework Equations





The Attempt at a Solution


I can't figure out how do i solve it. Using graphs as well, I could not arrive at any conclusion.
 
Physics news on Phys.org
The question is incomplete. Please post the full question
 
No, @adjacent, the question isn't incomplete. We have to fill in the blank. "the acceleration varies with x as ________ ". Sorry for not mentioning it clearly!
 
ritik.dutta3 said:
No, @adjacent, the question isn't incomplete. We have to fill in the blank. "the acceleration varies with x as ________ ". Sorry for not mentioning it clearly!

When you are given the position as a function of time, how do you find the acceleration using derivative?
 
My suggestion:
First take second derivative of x with respect to t to get acceleration which we will call z.
Then use dz/dx = (dz/dt)/(dx/dt)

Looks messy, but technically correct. In the final result, substitute for x where it appears.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Why would this be accelerating positively?
Replies
6
Views
963
How Does Acceleration Vary with Distance in s²=at²+2bt+c?
Replies
1
Views
971
Kinematics: Acceleration of a figure skater changing direction
Replies
16
Views
1K
Calculus Problem: acceleration, speed, and displacement of a particle
Replies
1
Views
2K
How Do You Calculate Total Displacement in Multi-Stage Motion Problems?
Replies
3
Views
1K
How force on atom in diatomic molecule varies with distance
Replies
12
Views
1K
Confused about kinematic equations
Replies
20
Views
2K
Kinematics Equations: Displacement Calculation with a Wheel | Homework Help"
Replies
8
Views
2K
Instantaneous Acceleration Given Equation for Velocity
Replies
7
Views
1K
Find the height of a lamp based on the velocities of projectiles
Replies
40
Views
2K

Hot Threads

Recent Insights

Back
Top