Mechanics A Level Question...?

Question

OK, so here's the question, I've had some difficulty answering it...

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=0, t=4, t=6 respectively. Modelling the car as a particle find it's acceleration and its velocity.

The answers are..

acceleration = 3 and a third m/s/s

Velocity = 13 and a third m/s

But I need to have the working for it too.

Thanks :D

Answer 1

i got a wrong answer oops

Answer 2

Let a be the uniform acceleration,x the distance travelled,

& t the time needed,then

d^2(x)/d(t)^2=a=>

dx/dt=at+c1=>

x=at^2/2+c1t+c2 where c1 and c2 are consts

When t=0,x=0=>c2=0,

when t=4s,x=80m=>

80=8a+4c1=>

2a+c1=20------(1)

again, when t=6,x=140m=>

140=(36/2)a+6c1=>

9a+3c1=70----(2)

Solve (1),(2) simultaneously,get

a=10/3 m/s^2 &

c1=40/3

So, the model is x"=a=70/3,&

x'=(10/3)t+40/3