The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (b) Calculate the velocity and acceleration vectors of the bird as functions of time.

Video transcript

Welcome back everybody. We are given the X and Y coordinates right here of an insect flying. And we are asked to find what the x and Y components of the velocity and what the X and Y components of the acceleration are. Well, the derivative of X or X component is going to equal the X component of our velocity and the derivative of our x velocity component is going to equal the X component of our acceleration. Now the derivative of our Y component is going to equal the Y component of our velocity and the derivative of the Y component of the velocity equal the y component of our acceleration. We are given that the X component is 3.5 t. and the y component is four minus 1.5 T squared. Now let's go ahead and find our velocity and acceleration Velocity equal to well let's first find the ex opponent. So the derivative of this with respect to time is 3. will be multiplied by our I unit vector plus derivative of our Y component, Which is going to be -2 times 1. T. Which this equals 3. i -3 T. Yeah, Great. Now let's go ahead and find our acceleration, acceleration with respect to time would be the derivative of this component which is just zero since 3.5 is constant and then plus the derivative of this component or this component right here which is just going to be negative three. This is going to equal negative three. J. So now we have found our acceleration with respect to time, in our velocity, with respect to time, which corresponds to answer choice. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.