Oooh Mike thats not the right camera ! Mine is DSCH20 ! I wondered why the manual wasn't the same !
Yup I did wonder when I spotted your parallel post in 'Talk Basics' =
Action Shots
I also think I found the manual for your camera and linked to it there.
You do have some manual modes you can use to force the camera to use higher shutter speeds, if you check the book to find aproprioate menu selections.
However, I think that primary problem here at the moment is you are trying to cram too much dog in your frame, and using too much 'zoom', and possibly going right to the extreme and into the cameras 'digital' zoom.
More magnification you use... and zoom is magnifying the subject in the frame, isn't it? More you will magnify any errors.
Dogs are moving, and even at incredibly high shutter speeds, you will still get some 'blur' its caused by reletive movement between the camera and the subject... subject moving and or camera moving. Lower the shutter speed, more movement you are going to 'see' and have blurr in the frame. BUT bigger the subject, more of the frame that movements going to blurr over.
Meanwhile Digital Zoom... your camera has a 10x optical zoom from I think its 6.3mm to 63mm; when you touch the button, what makes the subject bigger on the screen, is bits of glass physically moving inside the camera, magnifying the image falling on the cameras sensor.
When you run out of 'zoom' in the mechanical world... the camera 'cheats'.
Your pictures are, 10Mpix? I dont know. They are made up of a grid of coloured squares any way. Millions of them. Probably something like 4,000 squares wide, by 3,000 squares tall. Generated by a sensor that has, for the purposes of this explanation, a grid of 'receptors' with one receptor for each pixel.
Now, when you run out of propper, optical zoom, the image on the sensor magnified as far as the lens will allow; what the camera does to 'Digital Zoom' is look at the middle bit of what is on the sensor..... maybe a grid just 2000 squares by 1,500... then it does some maths... 'processing' (Remember comment above about slowing the camera down, when the screen goes grey? Thats what happens when it has a lot of work to do, and this is giving it more work)... does some maths... and quarters the actual squares its looking at, and makes more 'best guesses' what to put into them, based on whats in teh squares around, to artificially magnify the image a bit more.
And digital zoom is almost ALWAYS blurry.... instead of the full 10 or 12Mpix image you're sensor might deliver, you are effectively looking at a 5 or 6Mpix image, thats been magnified 2x...
And what does magnification do? Thats right, magnify any errors! So you are looking at an image of reduced resolution, magnified to show it in all its possible horribleness!
Use less zoom. And avoid Digital zoom like the plague.
If you don't fill the frame with as much dog...... you wont magnify as much blurr. You may not get as big a pooch, but it will be sharper. Smaller subject = less frame for subject to blurr across.
Then the bonus's start stacking up. Not using as much zoom, you will be getting light from more of the scene*, you are looking at, which means the camera can set a higher shutter speed. Means less blurr still.
Tracking? Keeping the mutt in shot? Smaller in the frame, more space around it; so the more 'margin' you have and the less likely the mutt will run out of it while you are taking a picture.
Not using digital zoom? Less processing. Camera will spend less time thinking about writing data from sensor to memory card; you will get less shutter lag and more real-time screen viewing to keep tracking the dog.
Start with the simple..... use less zoom!
Then you can start thinking about how to force the camera to use higher shutter speeds, or other techniques at your disposal.... reading up on them, and then checking the camera user guide to see how to do them...
and
Then you can start thinking bolded.... because of comment in parallel thread, where you asked about an alternative camera that can do the thinking for you..... see reply there.
MACHINES DON'T THINK - They Merely Follow Instructions.....
YOU have to do the thinking. And it doesn't take much, once you have the idea.
* Contentiousely over simplified comment.
But you have a scene, iluminated by sunlight. More area of scene you have in the frame, so the more light you are catching on your cameras sensor. Imagine you have a torch in your hand.... shine it on a table so it lights up an area about the size of a dinner plate.... probably be bright enough to eat by. Shine it at a key-hole? Smaller area, probably be very bright, certainly enough to get your car key in the hole without scratching the paint on the door..... Now point it accross a field.... you probably wouldn't light up the hedge the other side of it, or if you did... wouldn't be very bright!
Same thing but backwards. Instead of a torch chucking out light.... you are holding a camera trying to 'catch' light. Point the thing down the field, trying to catch all the light falling on trees and hedges and grass and 'orses or whatever... lots of things all reflecting a lot of light at your sensor. Point the thing at a key-hole, and your sensor is only going to get that bit of light reflected from something the size of a coin... it ent going to be much, compared to something bigger than a house. (Research the Inverse Square Law)
Now! Contension of statement, is because in photography, to keep the maths simple, when we work out 'exposures'... we use ratios rather than actual quantities.
And significantly when we talk about 'aperture', which is a hole that lets light through the lens; rather than talking of an aperture setting in how BIG it is, I dont know, 0.25mm or whatever... we talk in f-stops; f1.4, or f3.6 or whatever... which is a RATIO of the the lenses focal length to the aperture diameter; and provides a sort of 'constant' that works whatever zoom setting we have; as the more zoom we use, the longer the focal length... to the bigger the aperture would be in mm to keep the same f-number... letting in more light, to compensate for the lesser amount of light the camera can 'see'... make sense?
So zoom ought not change your exposure; ISO to F-Stop to Shutter speed.
EXCEPT... on YOUR camera, and most modern zooms.... it does!
Because the 'maximum' aperture setting, the 'widest' aperture tends to be a smaller ratio at the wide angle end of the zoom, because its a ratio, and the apperture control on a lens can only make the hole smaller. So at the wide end you get one ratio from the biggest hole, at the other, as the focal length is increased, you get a different ratio, a higher F-number as the focal length you are dividing by the diameter of the biggest hole you can make, gets bigger.
So... the 'it doesn't matter what zoom you use' argument is based on the f-number not changing.....
Lens I have in front of me, is an 18-55mm f3.5/5.6. Maximum f-number at 18mm wide angle is f-3.5, at the 55mm telephoto end, its f-5.6.
If I were to meter on a scene, and got suggested exposure settings of say, f8 at 1/125th of a second, at ISO100.... I could zoom back and forth through the range, and those settings wouldn't change.
However, IF I set, f3.5.. that is three & 1/3 stops 'up' from f-8, so for same scene I could select a shutter speed of 1/600th, at ISO100 and keep the same exposure value.
BUT I would ONLY get f-3.5 at the 18mm zoom setting... as I zoomed 'in', the widest aperture the camera could set would get smaller, and at 55mm I would have f-5.6, two and a third stops 'down' from f-3.5.... so if I was using fully manual, and didn't change any settings... my picture would come out 'dark# two and a third stops 'under exposed', probably enough for it to be too dark to see anything useful.
So, I would have to 'compensate' and adjust either the ISO or the Shutter speed, to keep the same picture brightness or exposure.... and that would mean coming back down on shutter speed to about 1/250th.
HEAVY explanation... but there you go.
Your camera I think, has an f-3.5/4.4 maximum aperture; so same deal applies. Less zoom you use, faster the maximum aperture you have, higher your shutter speed might be set for the same exposure.
And I think from comment I read in review; you dont actually have any aperture control on your camera, it is fixed, and ONLY varies with the zoom, so likely you will ALWAYS have this issue, of more zoom meaning slower shutter.