I have a Peugeot 107 which is a 1 liter engine car.
I was wondering what is the maximum safe speed at different gears?
The car starts to make a lot of noise in 1st and 2nd gear, even at 10 mph at 2nd gear the car makes too much noise.
Your car has an engine designed with city based environments in minds so you will have a short gear ratio meaning you will have to shift lot of gears in the city but on the other hand car will be economical.
To determine optimal shifting time you need to look at the power graph of your car, the picture below shows the dyno of your car.
If you follow the the bottom line you can know that your car produces peak HP at around 3000 RPM so if you want better acceleration and performance shifting at around 2800 to 3000 RPM will be optimal.
However if you want economy shifting at 2000RPM will prove much efficient.
The speed however depends on the load the car is carrying and other factors which is not possible to theoretically determine. You need to observe that and shift accordingly.
It is never recommended to change gears at the maximum RPM for a city car since you will get very very less gas mileage and is harmful for your engine in the long run.
After all that, Changing gears still depends on a lot of factors which can only be determined by you when you drive, as a bonus I googled and got the below info on your car's shifting speeds.
I cannot gurantee authenticity of the below information and i do not endorse the below speeds Just use for reference
1 st gear : as short as possible
2 nd gear: to 35/40 max
3 th gear: 40-60km
4 gear : 60-85
5 gear : 70-> km