How do I find the speed of a vehicle when all I know is the length of the skid marks 24.2 metres and the pavement was wet at this time with a very slight slope down?

Answer 1

To find the speed you would need to find the time taken to create the skid marks and then use the equations of motion.

As the vehicle is skidding, the wheels are not turning so the braking force is the friction between the tyre and the road surface; this has to overcome the forward speed of the vehicle and the forward force of the weight of the vehicle along the road (as there is a downward slope).

The forward force of the vehicle can be calculated by knowledge of the mass of the vehicle and the angle of the slope.

The frictional force generated can be calculated from the coefficient of friction between the tyres and the road surface, and the mass of the vehicle. The road being wet will reduce the coefficient of friction of the road surface/tyre boundary compared to when the road surface is dry.

It is easier, by experiment, to do a few test runs using a vehicle of similar mass under similar conditions to get how the vehicle is likely to have slowed down when it skidded, and extrapolate/interpolate to the given distance of 24.2 m.

Answer 2

Not enough information for an exact calculation. You would have to get some information to get a reasonable ESTIMATE about the typical acceleration under these circumstances, then use the standard formula for acceleration.