 When a moving car suddenly applies brakes, it starts to skid over or slide over the surface on which it is moving, just like this. These are skid marks. And the car could be applying a brake for any reason. There could be some other car in front of it, it does not want to collide, there can be a person. And sometimes, unfortunately, accidents do happen. And investigators can actually determine the speed at which this car was moving just by measuring the length of the skid marks and also getting a sense of how much friction there was between the tire and the road surface. In this video, we will understand how do investigators actually do that. How do investigators determine the speed with which this car was moving before it started skidding. So here we have the car which is moving to the right. And when you apply the brake, suddenly the tires stop rotating, they start skidding and let's say after skidding for a certain amount of distance, it comes to a stop. And this right here is the skid mark. So in this situation, we do not really know the initial velocity, but we know the final velocity. And also we can measure the length of these skid marks. So let's say the length of these skid marks, this is 10 meters. Now you might be thinking that there will be a skid mark from the right tires and there will be a skid mark from the left tires. This can measure the length of both of those skid marks and then take an average. So this kind of looks like this. The skid mark length from the right tires plus the skid mark length from the left tires divided by 2. And let's say that this distance is approximately 10 meters. We do not know how much time the car took to stop. We also do not know any acceleration that is involved. But investigators do actually try to figure out the acceleration that the car faced and the car will be facing an acceleration in the opposite direction. They can actually figure this out. So this acceleration, this acceleration really depends on how much frictional force there is between the tire and the road surface. If the road surface is extremely rough, you can imagine that applying a break will try to stop the car even sooner because there will be a lot of frictional force on the left direction, in the left direction. So frictional force really depends not just on the road surface. It also depends on the type of tire that you are using. So it depends on both the tire, both the tire and the road, both the tire and the road. And by taking into account these two factors, investigators calculate something called as a coefficient of kinetic friction. They calculate something called as a coefficient of kinetic friction. This coefficient gives a measure of the frictional force between the tire and the road. And as a result of that, investigators can try and figure out the acceleration that the car faced. We will not go into how exactly they measure the coefficient of kinetic friction and the frictional force and the acceleration because it involves some knowledge of Newton's second law and how to balance forces and what is a frictional force. In this video, we can just say that the acceleration turns out to be approximately 8 meters per second square. Because most of the tires and most of the roads are made of the same material, right? Most of the time. So we can say approximately this is 8 meters per second square. Now we know three variables. We know final velocity, distance of skid marks, acceleration that the car faced. And we do not know the initial velocity, which is what we are interested in. We do not know time. So we can choose a kinematic equation which is independent of time, which does not have the variable t and has all of these acceleration, initial, final and distance. So it turns out we can use this equation v square. This is equals to u square plus 2 As. And final velocity is 0. Initial is something we need to figure out and acceleration because it's in the opposite direction to the movement of velocity. And we can say we can take a coordinate axis. We can say that this direction is positive y and this direction is positive x. So velocity was always in the positive x direction, but acceleration is in the negative x direction. So this will be a negative, negative number. So this becomes minus 2 into 8, 16 into 10. This is 160. And when we work this out, u really comes out to be equal to under root of 160. And this comes out to be equal to 12.6 meters per second. If we convert this in kilometers per hour, this is 45.4 kilometers per hour.