Longer focal length magnifies the image, which also magnifies subject movement and camera shake. An Image Stabilization feature can help to minimize camera shake, but it does not help subject motion. To minimize blur from camera shake, 35 mm film format (size) has an old rule of thumb that minimum handheld shutter speed should be at least:
If a 200 mm lens, then at least 1/200 second shutter if handheld.
But for sensors smaller than full frame (smaller than 35 mm film), this would be
If 1.5x crop and 200 mm lens, then at least 1/300 second shutter if handheld.
This about the crop factor is because the same viewing size must enlarge a smaller image that much more, which also magnifies the shake. People vary in their ability to hand-hold the camera still enough, so this is just a rough general notion, a little crude, and doubling this shutter speed is never a bad plan (double the divisor for half shutter time duration). "Thinking" about holding it steady during the exposure always seems a big help. But if pondering why your images are not sharp enough, check the shutter speed and focal length in the Exif. Using a speedlight flash can also be a big help to freeze any motion. We should always be thinking about reducing camera shake. It is what tripods are for.
If you don't know sensor dimensions, the calculator's second megapixel choice will compute them.
If you don't know crop factor, another calculator will compute it for cameras without interchangeable lenses from the lens specifications in your camera manual.
I'm just playing with the subject of camera shake. The calculator is accurate, but it's just a novelty, not really numerically useful since we don't have numbers for how much camera shake there was. But we might estimate subject motion speed and distance. The point it hopes to make is about realizing that slight camera shake can have significant effect at the sensor. A faster shutter speed can help freeze it.
Greater focal length magnifies motion at the sensor, but greater distance reduces it. Half the distance is seen at the camera as twice the motion, but twice the distance is half the motion (as seen at the camera). A plane flying 450 miles per hour at 25000 feet has very small motion blur in 1/100 second (as compared to diameter of DOF CoC limits). But a person walking by at 10 feet has tremendously more blur.
Subject motion speed can be calculated as pixels of blur. Subject motion sideways across the camera has the maximum computed effect. Subject motion at 45 degrees to the lens axis has about 70% effect. Subject motion directly towards or away from the camera is just a size difference, but which as "motion" will have relatively little effect during shutter speed duration (meaning twice the shutter time is twice the sideways motion, but twice the time forward is NOT half of the camera distance, depending on an extremely close distance maybe, but it is generally much less perceptible as motion).
You can enter a guess of how much motion might occur (how much the subject image moves out at the distance), or the second option will compute motion travel at a subject motion speed rate for a duration (shutter speed). The default "1/16 inch" motion shown is to be the blur motion (seen at the subject), which we might be able to guess at in the picture. I realize we may not know those numbers, but it might be fun to play with, to get an idea about the effect of motion (the specific goal is to actually realize how much it matters). We should always be thinking about reducing camera shake.
Do note the initial default case shown, that with a 50 mm lens seeing 3 MPH motion at 10 feet, in 1/250 second the subject moves 0.211 inch (0.101 degrees) which is 22.5 pixels of blur on this default sensor, and is 4.47x the standard CoC maximum limit that we still (barely) consider acceptably sharp. Then using that motion speed, the duration will compute the same movement for other shutter speeds i.e., double shutter speed will be half the motion). Or, the current default of 1/16 inch motion is specified as 1/16 inch movement regardless of shutter speed (the shake might be back and forth for example).
Another example: With a 1.5x crop factor sensor with 24 megapixels, and with sideways subject motion past the camera with 105 mm lens, moving at 20 MPH at 50 feet out, then 1/250 second shutter records 62 pixels of blur trail (12.3x CoC), but a 1/2500 second shutter records 6.2 pixels of blur and 1.23x CoC (ten times shutter speed is 1/10 the motion seen).
The comparison to CoC is in reference to Depth of Field standards. The blur circle at the extremes of allowable Depth of Field distance is called Circle of Confusion (CoC). 1x CoC is Not sharp, but is the maximum blur we might tolerate. The subject is hopefully sharper, but CoC is the largest blur considered perhaps acceptably sharp in Depth of Field limits. Motion blur is not related to focus, but CoC is an existing standard of sharpness, and it is used a size reference here. Blur computed to be 2.78x CoC is 2.78 times larger than the maximum 1x that Depth of Field would call marginally acceptable. CoC is discussed more with the DOF calculator here .
We do have a rough general rule of thumb about the necessary handheld shutter speed that will usually freeze typical motion in continuous light (like daylight or incandescent). It specifies that the shutter speed should be at least 1 / Focal length as seconds, for example, 1/100 second minimum shutter speed for focal length 100 mm. That was the rule for 35 mm film, and for digital, it should be 1 / Equivalent Focal length (focal length x crop factor, or 1/150 second for crop factor 1.5 with the 100 mm lens in this example). It is only a rough guide, because people vary in what they can reliably handhold steady. Some may hold steadier, and some are worse. "Thinking" about holding it steady during the exposure always seems a big help. Camera image stabilization methods (Nikon VR, Canon IS) help handholding with slow shutter speeds (allowing up to two or three stops slower), but it has no effect on subject movement. Tripods are good for camera shake, and speedlight flash is good for any motion.
One advantage of using the speedlight flash is that its light duration is very fast (for example, maybe 1/2700 second if at 1/4 power level), where the shutter speed might be 1/60 to 1/200 second (perhaps 45 to 13 times longer illumination for the motion to blur things). And the speedlight is much faster at lower power levels (for closer work). The speedlight flash can be fantastic for stopping motion, either subject motion or camera shake (like for macro work, handheld in the field). See more about use for High Speed Flash Photography.