The position of a particle as a function of time is given by 𝓇 = ( 5.0î ＋4.0ĵ )t² m where t is in seconds. b. Find an expression for the particle's velocity v as a function of time.

Video transcript

Hey everyone. So this problem is dealing with vectors. Let's see what they're asking us. We are told that displacement is directly proportional to velocity and inversely proportional to time. They give us this equation V equals D over T. We need to assume that the particles initial position is at the origin and that its final position changes over time by this given function they tell us T is in seconds. And then they ask us to write an equation that shows the velocity of the particle as a function of time. So we're given the position as a function of time and asked to find the velocity. So what we need to do here is recall that the velocity is the rate of change of position over time. And the way that we write that in math form is that V equals D R D T. So we're going to take the derivative of this position function to find our velocity function. So V of T equals For I plus two J times T squared D T. And so when we take the derivative of that, we are left with two Times for I plus 2J what times T, and we'll multiply that two throughout And come up with eight I plus four J times T and we went from units of meters when we derived that as a function of time, we are now working in meters per second. And so that's the answer here. So we look at our potential choices and we see that aligns with answer B that's all we have for this one. We'll see you in the next video.