For our first example of motion in a plane, suppose you are operating a radio-controlled model car on a vacant tennis court. The surface of the court represents the x-y plane, and you place the origin at your own location. At time t1=2.0s the car has x and y coordinates (4.0 m, 2.0 m), and at time t2=3.1s it has coordinates (7.0 m, 6.0 m). For the time interval from t1 to t2, find (a) the components of the average velocity of the car and (b) the magnitude and direction of the average velocity.

1) Suppose you reverse the car’s motion, so that it retraces its path in the opposite direction in the same time. Find the x-component of the average velocity of the car.

2) Find the y-component of the average velocity of the car.

3) Find the magnitude of the average velocity.

4) Find the direction of the average velocity.

he made 11 calls in one day

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .