A force in the +x-direction increases linearly from 0 N to 9000 N in 5.0 s, then suddenly ends. (b) What impulse does this force provide?

Video transcript

Hey, everyone. So this problem is working with impulse. Let's see what it's asking us. A box is pushed along a frictionless surface by a force that starts at zero newtons and increases linearly with time. And the positive X direction over a period of eight seconds, the force increases to 400 newtons after which it ends abruptly. What is the impulse delivered by the force to the box during this time? Our potential answers are 1320 I Newton seconds. B 1540 I Newton seconds, C 1480 I Newton seconds or D 1600 new 1600 I Newton seconds where I is in the positive X direction. OK. So this is a fairly straightforward problem if we can recall our impulse um equation. So our impulse J is equal to our average force multiplied by delta T. And so in turn, our average force we can recall can be calculated by our final force plus our initial force all divided by two. And then delta T is our teeth final, sorry T final minus T initial. And so when we look at each of these variables, our final force was given to us in the problem as 400 newtons, our initial force is zero newtons. Our final time is given as eight seconds. And so our initial time is zero seconds. So this term is zero, this is zero. And so we are left with our impulse equals 400 newtons divided by two multiplied by eight seconds or 1600 newton seconds. And this is all positive. So it's going to be in the positive X or positive I direction. And so that is the answer to this problem and that aligns with answer choice D. So that's all we have for this one. We'll see you in the next video.