In relativity theory, velocities can be represented by points in a certain "rapidity space" in which the distance between two neighboring points is ds = [2/(1 r2)]./dr2 r 2 d02, where r and 0 are polar coordinates, and we consider just a two-dimensional space. (An expression like this for the distance in a non-Euclidean space is often called the metric of the space). Use the EulerLagrange equation to show that the shortest distance from the origin to any other point is a straight line.

Very large accelerations can injure the body, especially if they last for a considerable length of time. one model used to gauge the likelihood of injury is the severity index ( ), defined as =/ . in the expression, is the duration of the accleration, but is not equal to the acceleration. rather, is a dimensionless constant that = the number of multiples of that the acceleration is equal to. in one set of studies of rear-end collisions, a person's velocity increases by 13.7 km/h with an acceleration of 36.0 m/s2 . let the + direction point in the direction the car is traveling. what is the severity index for the collision?

=force × distance a. work b. velocity c. pressure d. momentum

Which accurately compares concave and convex lenses?