Help Incline Plane Acceleration Vehicle Friction Distance

[istodorov]

Hello. I am new to this forum. I am a chemist. Physics is not my strength. Recently, I got a speeding ticket and I have to do some simple calculations in order to silence my mind. The problem is the following:

A car (m = 1498.95 kg) is constantly accelerating uphill (15 degrees incline) from:

a) 0 to 43 mph (69.2 km/h)
b) 5 to 43 mph (8 to 69.2 km/h)

The road is wet and it is snowing.

Static and dynamic friction coefficients are 0.6 and 0.4, respectively.

The acceleration time of the car from 0-60 mph (0-97 km/h) on a dry road is 8 seconds.
The acceleration time of the car from 0-43 mph (69.2 km/h) on a dry road is 5.73 seconds.

What distance the car would travel in both cases?
Is there any other data that I have to provide? Can you also include the equations that have to be used in order to solve this problem? Thank you so much!

 

[Delphi51]

This is an odd problem. Why would the distance the car travels be limited? If it can get sufficient grip on the road to accelerate, it should be able to keep on going at that same acceleration until something radical happens, such as reaching the top of the hill, running out of gas or exceeding the speed of light. Surely the answer is either zero or infinity for the distance.

It would be interesting to calculate the accelerations in the two cases, perhaps using
v = .5at^2. Also interesting to see what maximum acceleration the grip (friction) allows on the 15 degree hill. That is a complicated problem involving the component of the force of gravity acting down the hill as compared to the force of friction.

 

[istodorov]

The car accelerates to 43 mph and stops accelerating. The critical point that I released the gas pedal and the the car was moving due to inertia. I made left turn and started accelerating uphill in these conditions (wet snow i.e. a lot of friction) I want to know is it is physically possible a car with this mass to accelerate to 43 mph in a 15 uphill in about 250-350 feet where the police car moving towards me clocked me with this speed.

 

[Vanadium 50]

A 15 degree incline is enormous. That's a 27% grade: it ascends just under 100 feet over the length you are discussing.

To compare, the steepest grade on a paved road in the US is (according to the web) 13%.

 

[istodorov]

I am sorry. I've mistaken % incline with degrees. It is 8 degrees. Approx 15 % incline