You have a remot-controlled car that has been programmed to have velocity v = (3ti + 2t^2j) m/s, where t is in s. At t = 0 s, the car is at r0 = (3.0i + 2.0j) m. What are the car's (a) position vector

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Hi, everyone in this practice problem, we're being asked to determine the position factor at time, T equals three seconds. We will have a car traveling on an interstate highway with the X and A Y components of the car's velocity given by the equation of V equals two T I plus nine T squared J meters per seconds. Assuming that the car's initial initial position are not at time. The knot is given by the equation of R knot equals five I plus three J meter. We're asked to determine the position factor at time D equals three seconds. The options are a four, I plus four JB I plus AJ C 14, I plus 84 J N D two I plus six J. So we're given the car's velocity uh initial position in two dimensional um factors. So cars velocity P T will follow the equation of two T I plus 9 T Squared J meters for seconds. And then the car's initial position are not, are going, is going to be equals to five I plus three J. Peter. So to find the position factor at time, T equals three seconds, uh what we need to do is to actually uh use the integral or find the integral of its velocity and input the T to equals to three seconds. Because we know that the position of an object can be obtained as the integral of its velocity. So RT will equals to the integral to of P T D T plus the initial position are not. So this will then actually be the integral of um 2 TI plus T squared J D T plus five I plus three J meter. The integral should then be solvable. So the integral of two T will equals to TT squared I. So this is going to be T squared I and then the integral of nine squared will then be um 3 TQJ just like so and we will still have our R knot which is going to be five I plus three J. And all of this are going to be in meter because we just solved the integral. Now, what we need to do is to input the T equals three seconds into our equation. So at T equals three seconds, T squared is going to be three squared I plus three, multiplied by three cube J plus five, I plus three J. Um solving for this, then this will equals to nine I plus five I plus um 81 J plus three J that will essentially equals to uh 14 I Plus 84 J and that will correspond to our position factor at time T equals three seconds. So at time T equals three seconds, the position is going to be at 14 I and 84 J which will correspond to option C in our answer choices. So option C is going to be the answer to this particular practice problem. If you guys still have any sort of confusion, please make sure to check out our adolescent videos on similar topics, especially on probably solving the integral and I'll be all for this one. Thank you.

You have a remot-controlled car that has been programmed to have velocity v = (3ti + 2t^2j) m/s, where t is in s. At t = 0 s, the car is at r0 = (3.0i + 2.0j) m. What are the car's (a) position vector

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Key Concepts

Velocity

Position Vector

Integration