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Unit Vector Example # 2
The object is moving according to the displacement vector function given in the above example. In other words, we can determine the displacement vector of our object at any given time by simply plugging in the time value and solving for our component vectors. (a) In the first part of the example, we are asked to determine both the velocity vector function as well as the acceleration vector function. In order to find the velocity vector function, we must take the first derivative of each displacement component vector function. Likewise, in order to determine the acceleration vector function, we must take the derivative of the velocity vector function. (b) Now, we must use what we obtained in part (a). We plug in a value of 2 seconds into the velocity and acceleration vector functions. We then determine the magnitude by using our formula (take the square root of the sum of the squares of the component vectors).