Hey, what's up YouTube? This is the engineering methods with the boy here, German. So today we will be looking at kinetics of particles and equations of motion. So our problem is we are required to determine the shortest time it will take the conveyor belt to stop without the box being shifted. Okay, so we are told that our box has a mass of 15 kilograms and the speed of the speed of conveyor belt is 3 meters per second. Okay, so we are required to determine the shortest time it will take the conveyor belt to stop without the box being shifted. Okay, so let's let's consider this statement without the box being shifted. So also we have our our coefficient of static friction, mu S, or mu S is 0.5. Okay, now we will go back to this statement and let's say without the box being shifted. So our free body diagram of our box will look like this. It will look like this. We have the normal direction force, the weight which is mg. And of course we have a force this direction and the force this direction, this is the speed, acceleration this direction because obviously the speed is reduced and so the acceleration will be in this direction. So from our free body diagram, since the resultant force in the Y direction is 0, we have our normal direction force being equal to mg. So for this box not move, the force, the horizontal force mA should be less, should be less than mu S n, which is the force. The normal force multiplied by mu, mu S reaches the static friction. So this condition will allow the box not to move when the conveyor belt is going to stop. And also notice that the final velocity of the conveyor belt will be 0 when it stops. So we are required remember we are to find the shortest time it will take the conveyor belt to stop without the box being shifted. So given this condition we will say our mA, mA which is 15 kilograms times A should be less than 0.51 multiplied by this is close to this which is mg, 15 multiplied by the acceleration due to gravity. Okay so from this we can find our acceleration. So acceleration is equals to 0.15, 9.81 divided by 5th of course is the cost of this. So acceleration should be equals or less than 1.147 meters per second squared. So we are going to consider the equations of motion, the one which will relate, spin, time, and acceleration. And obviously it will be VF is equals to V initial minus 80 because it is acceleration we have this negative side. So our final velocity we said is 0. So since our final velocity is 0 we have this and our initial velocity is 3 minus acceleration is 1.47 times t. So making our time the subject of the formula we have t is equals to dividing both sides by taking this 3 to the other side and dividing by the acceleration we have 3 divided by 1.47 which will give us the shortest time being 2.04 seconds. So this is the shortest time it will take the conveyor belt to stop without the box being shifted. So that's how you solve these kind of problems. And remember to smash the subscribe button and