A-level Maths Mechanics Question (M1 Kinematics)

[AngloScot]

I am struggling with the following question and cannot find help anywhere, could someone please help me out or give me a link or two? Cheers:) A, B and C are three points on a straight road such that AB = 80m and BC = 60m. A car travelling with uniform acceleration passes A, B and C at times t=0s, t=4s and t=6s respectively. Modelling the car as a particle find its acceleration and its velocity at A.

[sddsddean]

I think all the equations you need are here http://www.crocodile-clips.com/absorb/AP5/sample/010104.html

[Peter Pedant]

yeah OK DJ draw a line with A b and C on it Between ab is 80 and between BC 60 Vel va.......vb.....vc t 0 4 6 remember a is const and is to be found. using v=u+at, doncha get vb = va + 4a and vc = vb + 2a and using s+ ut + 1/2 at (squared) doncha get 80 = 4 va plus 1/2 a 4squared and 60 = 2 vb plus 1/2 a two squared which is all very well but now you have two velocities and an acceleration. Tht is three variables and two equations But but but you can generate a third equation with the whole distance 140 and the whole time (6s) to get (anyone else reading this can go to sleep by the way) 140 = 6 va + 1/2 a 6 squared three eqns, thre variables, I recdkon a is 20/6 and va is 13 1/3 and having solved it I got tired. Hope this helps

[bernardo]

The one I remember from O-level is

s=ut+½at²

which gives

80=4u + 8a
140=6u + 18a

which simplified are

20=u + 2a [1]
70=3u + 9a [2]

[2] - [1] gives
50=2u + 7a [3]
[3] - 2[1] gives
10 = 3a

therefore a=3 and a third [4]

Put [4] into [2] gives

70=3u + 30
40 = 3u

so u = 13 and a third.

[bernardo]

Which means that Peter Pedant and I agree with each other! Hooray!

by the way, I worked out my answer before reading the other answers

[AngloScot]

Peter and bernardo, you are both absolutely correct, bernardo's method was much easier to follow but just because thats the way i was taught to do simultaneous equations, thanks to both of you, great help.