# Formula for time to distance from stop

1. Nov 1, 2007

### jph

Can someone please post the formula I need to use to determine the time it takes for a vehicle to start from a stopped position on a paved asphalt roadway (coef of approx .70), a grade of +3 degrees, and accelerate to a known distance?

Thanks for any help.

jph

2. Nov 2, 2007

### Shooting Star

Is this a homework question? In that case, you write what you have done so far.

3. Nov 2, 2007

### HallsofIvy

Staff Emeritus
As stated this doesn't make a whole lot of sense. Since you give the "coefficient" (of friction?) I suppose we are to calculate the acceleration from force but you haven't told us the force exerted by the engine.

4. Nov 2, 2007

### Shooting Star

I think the vehicle is simply rolling downhill. Let the OP present the problem clearly.

5. Nov 2, 2007

### jph

Drive down

This is not for homework or a class assignment. I'm trying to resolve a hunch on how a motor vehicle accident happened. I believe it was intentionally created, called a "drive down."

I am aware of some speed formulas and can derive them from KE=FR.

I believe that there is a formula that will allow me to determine the time it takes for a vehicle to accelerate from a stop to a given distance, and that it is dependent upon the force, rate of acceleration, etc. and I likely may not be able to apply the formula without having many other parameters in place first. I am not sure of what all parameters I must have to derive the time in this case.

I do not recall the necessary elements needed for the formula.

I should be able to obtain them. I know the coef of the roadway, the grade of incline, and the distance the vehicle traveled prior to impact. I know the type of vehicle and can get the weight of the vehicle to an approximation.

Is there a formula, or am I searching for a pipe dream?

Thanks

6. Nov 2, 2007

### Shooting Star

Ooh, a mystery thriller!

The grade of just 3 degrees will be negligible, in compared to accelerations produced by cars.

I also presume the co-eff of friction is that for rolling friction. Otherwise, it’s of no use.

Assuming constant acceleration, d = (½)at^2. You can get ‘t’ from this, provided you know ‘a’.

The component of g along the road will be g*(sin 3 deg). The resisting force is 0.7*m*g so the deceleration will be 0.7*g due to friction.

The other component of acceleration has to be experimentally found. You may also get the maximum acceleration from the car manual, but I can’t see how you will know the actual value.

If you can figure out roughly the speed at impact, then you can know the accn by using v^2=2da.

7. Nov 2, 2007

Thank you!!