# Does a car's speed change during a turn?

1. May 16, 2015

### MarkPS

Imagine a car driving forward at constant speed. If the car would make a turn, each wheel would get its own speed since each wheel has its own radius to the center of the curve. But does the center of car's speed stay the same?

Here's a simulation I made: https://vid.me/HYz9 [Broken] The red arrow represents the center of the car's velocity, the green arrow is the front wheel's velocity. As I turn the wheel, the front wheel's speed get's bigger, but the center of the car's speed stays the same. Is this accurate?

The way I see it is that if a car drives straight at speed V, it then makes a turn, after the turn it straightens out and the speed will still be V. Obviously this only works if there is no forces that slows down the speed, which is assumed here.

Last edited by a moderator: May 7, 2017
2. May 16, 2015

### Orodruin

Staff Emeritus
This depends completely on the forces acting on the car. It is completely possible to have the car increase as well as decrease its speed during a curve depending on how hard you press the brakes and/or acceleration.
This is a tautology. You are basically saying "the car will not slow down unless there are forces acting in such a way that it slows down". The relation you might be after is this:
$$\frac{dv}{dt} = \frac{d\sqrt{v^2}}{dt} = \frac{1}{2\sqrt{v^2}} \frac{dv^2}{dt} = \frac{1}{v} \vec v \cdot \vec a$$
That is, the derivative of the speed is equal to the projection of the acceleration (and therefore proportional to the projection of the force) onto the direction of the velocity.

3. May 16, 2015

### MarkPS

I was a bit unclear, I'm not breaking nor accelerating. I'm just turning the steering wheel.

I realize the problem with that sentence. What I mean is that there is no air resitance and no friction in the wheels' directions. Obviously we need friction so that the car can turn.

So given that I only turn the steering wheel, I don't press the gas or break. The car is not affected by friction or air resistance, but it still can turn (lateral friction?). Is my simulation then accurate?

4. May 16, 2015

### rcgldr

If you make the assumption that there are no factors affecting linear acceleration (like rolling resistance effects related to side loads), then there's only centripetal acceleration, and in that case speed is not changed, only direction.

5. May 16, 2015

### at94official

very well said.