As far as I know, there are two kinds of acceleration, when one are moving in a straight line, and when one is going around a curve at constant speed. Calculating acceleration while moving in a straight line is easy: change in velocity/change in time. But how do you calculate the change in velocity when going around a curve?

Use vectors. Say you're going around a 90 degree turn; you're travelling at 40 mph when you enter the curve and 30 mph when you leave. You draw a line 40 mm long (that represents your initial velocity); from the start point of that line you draw another line at right angles, 30 mm long (your final velocity). You measure the line between the two heads--50 mm. That's the change in velocity (well, 50 mph). Now figure how much time it took.

In both cases, acceleration is the same. The derivative (change) of velocity with respect to time. The key to remember is that speed and velocity are not the same. Think of speed as how fast something is moving. Velocity is the combination of speed and direction. To to this, you need to use vector calculus, but the concept is easy to grasp. Since they represent magnitude and direction, vectors are frequently represented graphically as arrows (yes mathematicians have a much more specific definition of a vector, but this one will suffice for these purposes). For a velocity vector, the length of the arrow will give you the speed and the arrow will point in the direction of change of motion. Acceleration is also a vector. Vectors can be added and subtracted to yield vector sums and differences. Multiplication and division are a bit more difficult, but the end result is that you can treat vectors as numbers and calculate the derivatives that are needed to determine velocity and acceleration.

For uniform circular motion, the velocity vector of an object will be perpendicular to the circle and the acceleration vector will point to the center of the circle. Here is a graphical explanation of circular motion. For linear motion, the velocity and acceleration vectors will both be either parallel to the motion or zero. If you define your coordinate system to be parallel to the motion,you get the simplification that velocity = speed. The simplification with linear motion is that the direction can only be left ,right, or 0 (with the positive or negative sign serving to identify the direction), but with 2 or 3 or more dimensions, the direction becomes a little more difficult to conceptualize.

v^2 / r is your centripetal acceleration if it is "at constant speed" along a circular path (contant r).

If you accelerate along the path of a circle, use a delta v to get the average centripetal acceleration. [added...the (delta v)/(delta t) would be your acceleration rate along the path]

Daver, the 50 mph would not apply in this case as the 30 mph vector is not an addition to the 40 mph.

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Instantaneously, the acceleration when going a speed s around a curve with radius r is s^2/r. That's also equal to w^2 times r, where w represents the angular speed. That's the centripetal (directed towards the center of the circular curve) acceleration necessary to turn the object around the curve.

Notice, depending upon how you look at it, the acceleration is directly proportional to r (holding angular speed constant) or inversely proportional (holding linear speed constant).

Velocity has 2 components: Speed and Direction.

Speed is not velocity, speed is just one part of velocity. Don't confuse the two.

Acceleration is any change in velocity. The change in velocity can come from either the speed changing, the direction changing, or both speed and direction changing.

In the case of linear acceleration, the only component of velocity that changes is the speed, so it is easy to calculate the acceleration (as you figured out).

In the case of curved acceleration you have to know what is changing (direction only, or both speed and direction). In the case of constant speed around a curve, only the direction is changing, (so you have acceleration) and the formula that milli360 gave is accurate.

If BOTH speed and direction are changing at the same time (i.e. braking your car as you drive around a corner) then you add up both the centrepital acceleration and the change-in-speed / change-in-time acceleration.

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