Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    Soz this is a long one, feel free to only do some of the question if it's a bit much but i cant seem to get anywhere with it.

    Question:

    A particle P moves along the x-axis passing through the origin O at time t=0. At any subsequent time t seconds, P is moving with a velocity of magnitude v m/s in the direction of x increasing where:

    v = 2t^3 + 2t + 3

    a) Find the acceleration of P when t = 3
    b) Find the distance covered by P between t = 0 and t = 4.

    A second particle Q leaves O when t = 1 with constant velocity of magnitude 10 m/s in the direction of the vector 3i - 4j, where i and j are unit vectors parallel to 0x and 0y respectively.

    Find, as a vector in terms or i and j
    c) the velocity of Q
    d) the velocity of P relative to Q at the instant when t=1

    Hence
    e) find the magnitude of the velociy of P relative to Q when t = 1
    f) find the angle between the relative velocity and the vector i at the instant

    Answers... which I can't get
    a) 14 m/s
    b) 70 2/3 m
    c) (6i - 8j) m/s
    d) (i + 8j) m/s
    e) root 65 m/s
    f) 82.9 degrees
    Offline

    5
    ReputationRep:
    you have a typo which made my answer be wrong.
    v = 2t^2 + 2t + 3

    a) Find the acceleration of P when t = 3
    dv/dt = a
    v = 2t^2 + 2t + 3
    dv/dt = 4t + 2
    at t= 3
    a = 14 ms-1

    b) Find the distance covered by P between t = 0 and t = 4.
    S = int v dt
    v = 2t^2 + 2t + 3
    S = 2/3 . t3 + t² + 3t


    S = 2/3 . (4)3 + (4)² + 3(4) - 0
    S = 70 2/3 m
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by yazan_l)
    dv/dt = a
    v = 2t^3 + 2t + 3
    dv/dt = 6t² + 2
    at t= 3
    a = 56 ms-1


    S = int v dt
    v = 2t^3 + 2t + 3
    S = ½t4 + t² + 3t


    S = ½(4)4 + (4)² + 3(4) - 0
    S = 156 m
    Yeah, that's what i did but they are NOT the answers

    Answers

    a) 14 ms^-2
    b) 70 2/3 m
    • Thread Starter
    Offline

    14
    ReputationRep:
    Any suggestions?
    Offline

    18
    ReputationRep:
    A particle P moves along the x-axis passing through the origin O at time t=0. At any subsequent time t seconds, P is moving with a velocity of magnitude v m/s in the direction of x increasing where:

    v = 2t^2 + 2t + 3

    a) Find the acceleration of P when t = 3

    a = dv/dt
    a = 4t + 2

    t = 3
    a = 4(3) + 2
    a = 14m/s²

    b) Find the distance covered by P between t = 0 and t = 4.
    v = dx/dt
    ∫1 dx = ∫v dt
    x = ∫v dt = 2t3/3 + 2t2/2 + 3t

    At t = 0, x = 0
    At t = 4
    x = 2(4)3/3 + 2(4)2/2 + 3(4)
    x = 42.667 + 16 + 12
    x = 70 and 2/3m
    • Thread Starter
    Offline

    14
    ReputationRep:
    (Original post by Widowmaker)
    The book's answers are wrong.
    I'm not so sure though

    a = 56m/s² seems too high
    • Thread Starter
    Offline

    14
    ReputationRep:
    Thanks anyway...
    Offline

    5
    ReputationRep:
    according to the answers : v = 2t² + 2t + 3 not v = 2t³ + 2t + 3
    Offline

    5
    ReputationRep:
    now try to solve the other questions, if ur problem was that u werent able to get the book's answers
    Offline

    5
    ReputationRep:
    here are the answers for the rest of the question, they are in white if you wanted them:

    c) the velocity of Q
    10 (3i-4j)/sqrt[3²+4²] =
    10 (3/5 i - 4/5j) =
    6i - 8j


    d) the velocity of P relative to Q at the instant when t=1
    VP at t=1 = 2 + 2 + 3 = 7i
    velocity of P relative to Q = VP-VQ
    velocity of P relative to Q = 7i - (6i - 8j) = i + 8j


    Hence
    e) find the magnitude of the velociy of P relative to Q when t = 1
    |i+8j| = sqrt [ 1 + 8²] = sqrt [65]

    f) find the angle between the relative velocity and the vector i at the instant
    [email protected] = 8/1
    @ = 82.9o
 
 
 
Turn on thread page Beta
Updated: June 1, 2005

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19
Poll
Were you ever put in isolation at school?
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.