Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    How could you find acceleration from two distances and two times, i.e the question is: The distance OA is 64m and OB is 250m. The car passes point O at 0 seconds, A at 2 seconds and B at 5 seconds. Acceleration is constant. The car however does not have 0 velocity (U) at O because 'the car is emerging from a bend before it reaches O which is a straight piece of road'. How would you solve this to find acceleration and then the speed of the car at B. It is straight road. Thank you!
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by mayjb)
    How could you find acceleration from two distances and two times, i.e the question is: The distance OA is 64m and OB is 250m. The car passes point O at 0 seconds, A at 2 seconds and B at 5 seconds. Acceleration is constant. The car however does not have 0 velocity (U) at O because 'the car is emerging from a bend before it reaches O which is a straight piece of road'. How would you solve this to find acceleration and then the speed of the car at B. It is straight road. Thank you!
    Generate two equations for displacement (s) and then solve them simultaneously.

    Have a go and post your working if you get stuck.
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by mayjb)
    How could you find acceleration from two distances and two times, i.e the question is: The distance OA is 64m and OB is 250m. The car passes point O at 0 seconds, A at 2 seconds and B at 5 seconds. Acceleration is constant. The car however does not have 0 velocity (U) at O because 'the car is emerging from a bend before it reaches O which is a straight piece of road'. How would you solve this to find acceleration and then the speed of the car at B. It is straight road. Thank you!
    It is useful to split this into two different scenario's: motion for OA and motion for AB.

    OA:

    s=64

    u=u

    v=u+at

    a=a

    t=2

    AB:

    S=250-64=186

    U=u+at

    V=U+AT

    A=a

    T=3

    Can you see where to go from there?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by RDKGames)
    It is useful to split this into two different scenario's: motion for OA and motion for AB.

    OA:

    s=64

    u=u

    v=u+at

    a=a

    t=2

    AB:

    S=250-64=186

    U=u+at

    V=U+AT

    A=a

    T=3

    Can you see where to go from there?
    It's simpler to consider the motion for OA and OB, then you don't have to worry about the velocities.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by RDKGames)
    It is useful to split this into two different scenario's: motion for OA and motion for AB.

    OA:

    s=64

    u=u

    v=u+at

    a=a

    t=2

    AB:

    S=250-64=186

    U=u+at

    V=U+AT

    A=a

    T=3

    Can you see where to go from there?
    I completely understand what you've written but I'm not sure how to go from there as we do not know u???
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by mayjb)
    I completely understand what you've written but I'm not sure how to go from there as we do not know u???
    I recommend considering the motion in OA and OB.

    OA:

    s = 64
    u = u
    a = a
    t = 2

    OB:

    s = 250
    u = u
    a = a
    t = 5

    Use the s = ut formula for both to have two equations containing the unknowns s and u.
    • Thread Starter
    Offline

    1
    ReputationRep:
    [QUOTE=notnek;67523574]I recommend considering the motion in OA and OB.

    OA:

    s = 64
    u = u
    a = a
    t = 2

    OB:

    s = 250
    u = u
    a = a
    t = 5

    Use the s = ut formula for both to have two equations containing the unknowns s and u.[/QUOTE

    Sorry I am confused, can we only find an average speed for u, as the car is accelerating??
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by mayjb)
    I completely understand what you've written but I'm not sure how to go from there as we do not know u???
    You can use s=\frac{1}{2}(u+v)t and use substitutions for the final speed in terms of initial speed and acceleration.

    For OA:

    64=\frac{1}{2}(u+v)(2)=u+(u+at)=  2u+2a

    For AB:

    186=\frac{1}{2}(U+V)(3)=\frac{3}  {2}[(u+2a)+(u+2a+3a)]

    Tidy it up and you have two simultaneous equations in u and a to solve.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by mayjb)
    Sorry I am confused, can we only find an average speed for u, as the car is accelerating??
    I'm not sure what you mean. 'u' is the initial speed i.e. the speed at the exact point where t = 0.


    (Original post by RDKGames)
    You can use s=\frac{1}{2}(u+v)t and use substitutions for the final speed in terms of initial speed and acceleration.

    For OA:

    64=\frac{1}{2}(u+v)(2)=u+(u+at)=  2u+2a

    For AB:

    186=\frac{1}{2}(U+V)(3)=\frac{3}  {2}[(u+2a)+(u+2a+3a)]

    Tidy it up and you have two simultaneous equations in u and a to solve.
    This is overcomplicating things.

    64=2u+2a

    This can come straight from s=ut+\frac{1}{2}at^2 instead of using two SUVAT equations.

    And the second equation is simple if you consider OB instead of AB.
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by notnek)
    This is overcomplicating things.

    64=2u+2a

    This can come straight from s=ut+\frac{1}{2}at^2 instead of using two SUVAT equations.

    And the second equation is simple if you consider OB instead of AB.
    Meh, I wouldn't say using substitutions is very over complicating things, but okay, up to him what he wants to do as long as he understands the method he uses and does it correctly.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by RDKGames)
    Meh, I wouldn't say using substitutions is very over complicating things, but okay, up to him what he wants to do as long as he understands the method he uses and does it correctly.
    In this case I don't agree. Mechanics students should be encouraged to look for the simplest method to minimise errors.

    Most M1 students who try your method would end up in a mess. And there's definitely no need to use two SUVAT equations.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by notnek)
    In this case I don't agree. Mechanics students should be encouraged to look for the simplest method to minimise errors.

    Most M1 students who try your method would end up in a mess. And there's definitely no need to use two SUVAT equations.
    thanks for the help!
 
 
 
Poll
Who is your favourite TV detective?
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

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.