Mechanics

I have been stuck on this question..
"A car travels with uniform acceleration between three lamp posts, equally space at 18 m apart. It passes the second post 2 seconds after passing the first post, and passes the third post 1 second later.
I have written:
s=36
t=3
v=18
(i) Find acceleration.
I have got the answer : 4m/s^2 but this is wrong!

The question is guiding you to separate it into two parts.

Start at post 1 with acceleration a. In 2 seconds it does 18m. We have s, u, a... but we need 4 things for suvat! So let's introduce v, the final speed at the moment it is passing post 2. The reason for this is unclear st first but gets clear when you complete the question.

Now, can you set up the suvat values for post 2 to 3 in a similar fashion? There is one key difference that uses something we have set up in post 1-2.

Are my values correct?

I get 6 m/s/s

Not sure what your values are meant to represent. If it's the whole time period from the first to the last lamposts, then I agree with s=36, t=3, but I don't know where you got the v=18 from, as I make it 21.

I suggest posting your whole working.

The question said that it passes the third post 1 second after so I assumed the final velocity would be 18.

Could you talk me through how you got 21?

That would only work if the velocity was constant, however it is accelerating.



Start by working out a.

Use s=ut+(1/2)at^2 twice. Once for the first to second lamposts, and once for the whole thing - first through third.

You'll get 2 equations with 2 unknowns, u and a

Solve simultaneously - u=3 and a=6, if I remember correctly.

Then v=u+at for the final velocity.