How Do You Calculate Deceleration from Two Segments of Motion?

[Plantatree123]

Homework Statement

I am stuck with this task please help me.

1. A body is moving with constant deceleration while passing through path that contains two same parts and each one of them is 10m. The first part of the path, body passes for t₁= 1s and the second part passes for t₂=2.2s. Determine decelartion of the body!

Homework Equations

I assume :
First part of the path : s₁= v_ot₁- (at₁²)/2
Second part of the path : s₂= vt₂ - (at₂²) /2
V = Vo -at₁

The Attempt at a Solution

I tried to sum s₁ + s₂ because the whole path is s = s₁ + s₂ and then to find acceleration but this was not good because I left with initial velocity. I tried it many times but each time unsuccessfully.

 

[Doc Al]

I assume :
First part of the path : s₁= v_ot₁- (at₁²)/2
Second part of the path : s₂= vt₂ - (at₂²) /2
V = Vo -at₁

So far, so good.
Use the values given for the distances and times and you'll have two equations and two unknowns. Solve!

 

[Ssnow]

If you assume the same constant deceleration in both the paths It seems correct. You have two equation and two data to find $a$ and $v_{0}$, try to solve the system ...

 

[haruspex]

sum s1 + s2 because the whole path is s = s1 + s2

That's ok, but that's going from two pieces of information to one. As Doc Al says, you need to make the use of the fact that you know the two distances separately. Since in this case the two distances are the same, one interesting avenue to try is subtracting the two equations to produce another.

V = Vo -at1

That introduces yet another unknown, the velocity at the boundary. Can you think of another equation along these lines?

 

[Plantatree123]

Ive found it ! Deceleration is a= 3,4 m\s²

Thanks everyone for help