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(I) A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow.What is the skier's change in velocity?
(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?
(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
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welcome to our first example video on one dimensional dynamics. In this video, we're going to look at functions and how we can use them to investigate one dimensional dynamics. So I suppose we have a function. X of T is equal to 5 m per second cube times tech, and the question then becomes How can we find the force as a function of time? Remember, forces a function of time would be proportional to acceleration as a function of time. Therefore, what we want to do is find acceleration from our function here and then multiply it by whatever mass the object might have will just assume that the mass of the object in this case is M. So we take the first derivative which will give us 15 m per second cube times T squared and a second derivative believe us with 30 meters per second cube times T meaning that f of T is equal to mass M times 30 m for a second cube times team. So it's not that challenging to do this. All we have to do is take a few simple in derivatives. In this case, if he on the other hand, We wanted to say that we start with a function for the force and wanted to find position as a function of time. We could do that. So say we have a function F 50 is equal to. We'll just say some initial force times one minus t over a time big teeth. In this case, we're going to say that AT T equals zero. We have X. Is that position zero and it's at rest. And then we can proceed. Finding this, let's say we want to find, um X At T equals capital T. So in order to do that, we have to first taken. We want to convert this into an acceleration acceleration. It's gonna be equal to one over m times f of tea. So in this case, that will be equal to F not divided by M times one minus time t divided by this big T. And we're taking an integral here, which means we're going to say integral F T DT is equal to V. F. T. When we apply that through, we see that will take the integral of a constant, which means we're going to result with just a time t here minus one half times one over tee times t squared and we need to add in some constant here. In this case, the constant because we have teas in these two will mean that V At T equals zero is equal to the constant, which is just V nuts, that 0 m per second. So the constant in this case would be zero. Next, we'll take the integral V f T d T. We're going to do that from little t to this big T rather from T equals 02 Big t again notice here that when we take the anti derivative every term will have a tea in it. It would look something like this will have f not over em. Times one half t squared minus 1/6 TT Cube And again we would have some constant here. We're going to evaluate this from t two Big T. When we do that evaluation, the constant will go away. All the terms with little t will be zero at T equals zero and then we'll be left with X at Big T is equal to f not over em times one half Big T squared, minus 16 big tee times that cube so we could cancel a t here and have this just be 1/6 times t squared. So, uh, just some basic calculus here if you're struggling to keep up with the anti derivatives or with the fundamental theme of calculus, So for solving when we have a definite integral should definitely go back and take a look at some of the mathematics videos here. Or you can look at the review videos at the beginning of physics one on one.
Equilibrium and Elasticity