in this video we're going to look at how we can use forces to speed up or slow down an object thus changing the object's momentum we saw in the last video that momentum is equal to mass times velocity so if we had a two kilo particle that was traveling at five meters per second then its momentum would be two times five so 10 kilogram meters per second if we then applied a force to it though in the same direction as it was traveling and that would cause it to accelerate and speed up this increased velocity would mean that its momentum has also increased for example if it was now traveling at eight meters per second its new momentum would be two times eight so 16 kilogram meters per second to work out exactly how much force is required to cause this change in momentum we need to use this equation which says that the force is equal to the change in momentum divided by the time over which the change took place so if we knew that the hand had applied the force over a period of 0.5 seconds then to calculate the size of that force we'd first of all need to work out the change in momentum which would be 16 which is our final momentum minus 10 which remember was the initial momentum of the object before it was hit and this would give us a change in momentum of six and then we can just divide this change in momentum of 6 by the change in time of 0.5 and that would give us 12 newtons so the hand must have applied a force of 12 newtons another way to write this equation is like this where mv is the final momentum and mu is the initial momentum because v and u are the final and initial velocities of the object let's now try another question using this new equation calculate the force required to accelerate a 600 gram ball from rest to 14 meters per second in just 0.1 seconds so for questions like this that involve quite a lot of different values it's best to write out a list of everything that you know so we could say that the initial velocity is zero because the object started at rest its final velocity is 14 its mass in kilos is 0.6 and the time is 0.1 then all we have to do is plug all of these into our equation so we get 0.6 times 14 for the mv part minus 0.6 times 0 for the mu part and then divide all of that by the time of 0.1 so if we simplify all of that we get a final momentum of 8.4 minus an initial momentum of zero all divided by 0.1 giving us a force of 84 newtons as our answer now one area where this stuff is really important is during car crashes if somebody traveling in a car collides with a brick wall then their momentum is going to decrease to zero almost instantly this massive change in momentum means that any people inside the car will experience a huge force which can cause injuries like head trauma or spinal damage to reduce the chance of damage we need to try and spread this change in momentum over a longer period of time because this will reduce the force that they experience and so they're less likely to get injured in order to help them achieve this cars have to by law be built with a bunch of different safety features like crumple zones seat belts and airbags chrome pool zones are at the front and back of the car and can crumple on impact so that instead of stopping suddenly there's a small amount of extra time for the car to lose momentum as it crumples belts meanwhile have two functions one is to stop you from physically flying out of the car as it stops but the other is that they're slightly stretchy so that you slow down a bit more slowly and finally airbags also act to help you lose momentum more slowly this is because they're compressible like a pillow unlike the hard dashboard or steering wheel that you might hear otherwise lots of other safety systems work in a similar way for example helmets or crash mats the key thing to remember is that all of these increase the time it takes for the momentum to be lost which results in a lower force acting on the person and so reduces the risk of harm anyway that's everything for this video so hope you enjoyed it and we'll see you again soon