A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by v = [5.00 m/s − (0.0180 m/s3)t2]î + [2.00 m/s + (0.550 m/s2)t]ĵ. (a) What are ax(t) and ay(t), the x- and y-components of the car's velocity as functions of time?

Video transcript

Welcome back everybody. We have a self driving vehicle whose velocity is given by this equation with respect to time. And we are asked to find the X and Y components of its acceleration. Now it is important to note that the derivative of velocity with respect to time is equal to acceleration. So in order to find the X. Component, we will take the derivative of the velocities X. Component. And to find the Y component we will find the derivative of velocities Y components. So let's go ahead and do that. So first we're gonna start out with the derivative of velocities X. Component. This means we're going to take the derivative with respect time of three minus 0.270 t squared which gives us negative 0.8108. Now let's take the derivative of velocities Y component which is just going to be the derivative of four plus 0.450 T. Which is just equal to 0.450. Putting this all together for our acceleration with respect the time we have negative 0.810 T times our I unit vector plus 0.450 times R. J. Unit vector corresponding to our answer choice of the Thank you guys so much for watching. Hope this video helped. We'll see you all in the next one