The magnitude of this change in velocity  can be found with the Pythagorean Theorem and is equal to 14 m/s. You can see that the direction is 45° south of east.The acceleration is  = (14 m/s)/4 s = 3.5 m/s2 at an angle of 45° south of east.Looking at the vector diagram, you can see that this makes sense. To change from moving north to moving east the car needs a push in the southeast direction. If these were two velocities of a car moving in a circle, this would be average acceleration during one-quarter revolution. The direction at the midpoint would be directly toward the center of the circle. There is another way to calculate the acceleration without using vectors and without the need for the time. You can use an equation derived from an analysis of the circular motion. a
 If you know the speed of the roller coaster car and the radius of the circle, you can directly calculate the required acceleration. Knowing the mass, you can find the required force by using Newton's Second Law, F = ma. Sample Problem A roller coaster car moving at 12.0 m/s swings into a horizontal turn with a radius of curvature equal to 20.0 m
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