Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    To put it simply... I don't get it. :confused:

    I'm doing the OCR course and my exam is a week today, but I still can't get my head around integration...

    Looking at my notes, I have figured that:

    a (acceleration) integrates into v
    v (velocity) integrates into s

    I don't understand WHY this happens and I've searched the whole web and there is no AS site with anything about integration in the M1 area.

    Here's an example question... I have the answers so I'm not interested in them I want to know HOW you worked them out and WHY the logic you apply to them works.


    QUESTION:
    A particle P moves in a straight line so that, at time t seconds afer leaving a fixed point O, it's acceleration is -1/10t ms/\-2. At time t=0, the velocity of P is Vms/\-1.

    (i) Find, by integration, an expression in terms of t and V for the velocity P.
    (ii) Find the value of V, given that P is instantaneously at rest when t=10.
    (iii) Find the displacement of P from 0 when t=10.

    Thankyou for your time.
    Offline

    2
    ReputationRep:
    (Original post by Eye Jay)
    To put it simply... I don't get it. :confused:

    I'm doing the OCR course and my exam is a week today, but I still can't get my head around integration...

    Looking at my notes, I have figured that:

    a (acceleration) integrates into v
    v (velocity) integrates into s

    I don't understand WHY this happens and I've searched the whole web and there is no AS site with anything about integration in the M1 area.

    Here's an example question... I have the answers so I'm not interested in them I want to know HOW you worked them out and WHY the logic you apply to them works.


    QUESTION:
    A particle P moves in a straight line so that, at time t seconds afer leaving a fixed point O, it's acceleration is -1/10t ms/\-2. At time t=0, the velocity of P is Vms/\-1.

    (i) Find, by integration, an expression in terms of t and V for the velocity P.
    (ii) Find the value of V, given that P is instantaneously at rest when t=10.
    (iii) Find the displacement of P from 0 when t=10.

    Thankyou for your time.
    I'm not sure why it happens, but someone will probably tell you....as for the question:

    I'm not too sure what the acceleration is....I'm taking it as (-1/10)t rather than this -1/(10t) - i hope it's right

    (i) v = INT a.dt = -1/10 [ INT t dt]

    v = (-t^2/20) + c

    t=0, v=V
    so V= 0 + c, c=V

    v = V - (t^2/20)

    (ii) t=10, v=0
    so, 0 = V - (100/20)
    0 = V - 5
    so V = 5 m/s

    (iii) you can now re-write v as: v = 5 - (t^2/20)
    x = INT v.dt

    x = INT[5 - (t^2/20)]dt

    x = 5t - (t^3/60) + k

    t=0, x=0, so k=0

    x = 5t - (t^3/60)

    t=10, x = 50 - (1000/60)
    x = (100/3) m
    Offline

    10
    ReputationRep:
    (Original post by Eye Jay)
    To put it simply... I don't get it. :confused:

    I'm doing the OCR course and my exam is a week today, but I still can't get my head around integration...

    Looking at my notes, I have figured that:

    a (acceleration) integrates into v
    v (velocity) integrates into s

    I don't understand WHY this happens and I've searched the whole web and there is no AS site with anything about integration in the M1 area.
    Velocity is defined as the rate of change of displacement, so v = ds/dt (think about speed = distance/time, it's the same here).
    Acceleration is defined as the rate of change of velocity, so a = dv/dt (think about acceleration = change in velocity/time). Obviously integrating both those expressions wrt time will give you displacement and velocity.
 
 
 
Turn on thread page Beta
Updated: June 7, 2004

University open days

  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 30 Jan '19
  • Solent University
    Careers in maritime Undergraduate
    Sat, 2 Feb '19
  • Sheffield Hallam University
    City and Collegiate Campus Undergraduate
    Sun, 3 Feb '19
Poll
The new Gillette ad. Is it:
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.