Uniformly accelerated motion issue

[greg_rack]

Homework Statement

A car is travelling along a straight road with constant acceleration. It passes a road sign. It travels 12.2 m in the 3rd second and 14.4 m in the 4th second after passing the road sign. What was the speed of the car as it passed the road sign?
Result: [6.70m/s]

Relevant Equations

UAM law of time
a=Δv/Δt
v=Δx/Δt

I went quite confidently on this one, at least at the beginning...
I found the instant velocity on the 3rd second(v1=12.2m/1s) and the one on the 4th(v2=14.4m/1s), and subsequently the acceleration(a=2.2/1m/s*s).
Since the acceleration is constant, using the law "v=v0+aΔt", I have found v0 which in my case results as 5.6m/s as opposed to the 6.7m/s it should.
What am I getting wrong?

 

[PeroK]

Homework Statement:: A car is traveling along a straight road with constant acceleration. It passes a road sign. It travels 12.2 m in the 3rd second and 14.4 m in the 4th second after passing the road sign. What was the speed of the car as it passed the road sign?
Result: [6.70m/s]
Relevant Equations:: UAM law of time
a=Δv/Δt
v=Δx/Δt

I went quite confidently on this one, at least at the beginning...
I found the instant velocity on the 3rd second(v1=12.2m/1s) and the one on the 4th(v2=14.4m/1s), and subsequently the acceleration(a=2.2/1m/s*s).
Since the acceleration is constant, using the law "v=v0+aΔt", I have found v0 which in my case results as 5.6m/s as opposed to the 6.7m/s it should.
What am I getting wrong?

At what time in the third second did you calculate the velocity? At the beginning, middle or end of that interval?

 

[greg_rack]

At what time in the third second did you calculate the velocity? At the beginning, middle or end of that interval?

I supposed it ran 12.2m in one second, from the beginning to the end of the 3rd second interval.

 

[PeroK]

I supposed it ran 12.2m in one second, from the beginning to the end of the 3rd second interval.

The question tells you that. But, you calculated a velocity. At what time does that velocity apply?

 

[greg_rack]

The question tells you that. But, you calculated a velocity. At what time does that velocity apply?

That applies at the end of the interval, I'd say

 

[PeroK]

That applies at the end of the interval, I'd say

Are you saying that the car was traveling at $12.2m/s$ at the end of the third second?

 

[greg_rack]

Are you saying that the car was traveling at $12.2m/s$ at the end of the third second?

Oh, well, since it's a "mean" velocity, shouldn't it apply to the middle of the third second?

 

[PeroK]

Oh, well, since it's a "mean" velocity, shouldn't it apply to the middle of the third second?

Exactly!